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" Nee aranearum sane textus ideo melior quia ex se fila gignunt, nee noster 
Tilior quia ex alienis libamus ut apes." Just. Lips. Polit. lib. i. cap. 1. Not. 








" Meditationis est perscrutari occulta ; contemplationis est admirari 

perspicua Admiratio generat qufestionein, qusestio investigationem, 

investigatio inventioneni." — Hugo de S. Victore. 

— "Cur Spirent venti, cur terra dehiscat 
Cur mare turgescat, pelago cur tantus amaror, 
Cur caput obscura Phoebus ferrugine condat, 
Quid toties diros cogat flagrare cometas 
Quid pariat nubes, veniant cur fulmina ccelo, 
Quo micet igne Iris, superos quis conciat orbes 
Tarn vario motu." 

/. B. PineUi ad Mazonium. 





Dr. F. Auerbach on the Passage of the Galvanic Current 

through Iron. (Plate I.) 1 

Prof. S. P. Thompson and Dr. 0. J. Lodge on Unilateral Con- 
ductivity in Tourmaline Crvstals 18 

Mr. F. Guthrie on the Fracture of Colloids. (Plates 11. & III.) 25 
Professors J. Perry and AV. E. Ayrton on a neglected Principle 

that mav be emploved in Earthquake Measurements. 

(Plate lY.) '. 30 

Prof. D. E. Hughes on an Induction-balance and Experimental 

Researches therewith. (Plate Y.) 50 

Mr. W. C. Eoberts on the Examination of certain Alloys 

by the Aid of the Induction-balance. (Plate YI.) 57 

Mr. 0. Heaviside on the Theory of Faults in Cables 60 

Mr. N. D. C. Hodges on the Size of Molecules 74 

Dr. J. W. Draper on a new Form of Spectrometer, and on the 

Distribution of the Intensity of Light in the Spectrum .... 75 

On the Electric Light, by M. J. Jamin 81 

On the Deviations of Ampere's Theory of Magnetism from 

the Theory of the Electromagnetic Forces, by J. Stefan . . 83 
On the Production of Barium from Barium-amalgam, by Julius 

Donath, of Graz 84 


Dr. J. Kerr's Electro-optic Observations on various Liquids. 85 
Prof. H. A. Rowland on Professors Ayrton and Perry's new 
Theory of the Earth's Magnetism, with a Note on a new 

Theory of the Aurora 102 

Prof. Piazzi Smyth on Carbon and Carbo-Hydrogen, Spectro- 
scoped and Spectrometed in 1879 107 



Prof. J. J. Sylvester on an Equation in Finite Differences . . 120 
Mr. J. J. Hood on the Laws of Chemical Change. — Part II. . 121 
Prof. S. P. Thompson's Notes from the Physical Laboratory 

of University College, Bristol 129 

Mr. J. II. Birket on the Dissociation of Aniline Colours .... 136 
Dr. F. Auerbach on the Passage of the Galvanic Current 

through L'on 138 

Mr. S. Tolver Preston on the Possibility of accounting for the 

Continuance of Recurring Changes in the Universe, con- 

sistentl}'- with the Tendency to Temperature-Equilibrium . . 152 

Mr. O. Heaviside on the Theoi'y of Faults in Cables 163 

Kote on the Spectrum of Brorsen's Comet, by Prof. C. A. 

Young, of Princeton, N. J 178 

On Stokes's Law, by M. Lamansky 179 


Mr. M. M. Pattison Muir on Chemical Affinity 181 

Sir J. Conroy on the Distribution of Heat in the Visible Spec- 
trum 203 

Professors J. Perry and W. E. Ayrton on Structures in an 
Earthquake Country 209 

Dr. F. Auerbach on the Passage of the Galvanic Current 
through Iron 217 

Dr. J. Kerr's Electro-optic Observations on various Liquids. 229 

Sir G. B. Airy on the Construction and Use of a Scale for 
Guaging Cylindrical JMeasures of Capacity 246 

Mr. C. Clarke Hutchinson on a Convenient Source of Heat for 
Chemical Operations 250 

Notices respecting New Books : — 

Dr. G. Gore on the Art of Scientific Discovery, or the 
general conditions and methods of research in Physics 

and Chemistry 252 

Wheatstone's Scientific Papers 255 

The Action of Magnetism in Motion on Static Electricity, 
and Inertia of Static Electricity, by G. Lippmann 256 

On the Sensibility of the Organ of Hearing, by W. Kohlrausch. 257 

On a Direct Measurement of the Work of Induction, and a 
thence-derived Determination of the Mechanical Equivalent 
of Heat, by Dr. A. von Waltenhofen, of Prague 258 

On the Radiometer, by Dr. J. Puluj 259 


Lord Rayleigh's Investigations in Optics, with special refer- 
ence to the Spectrascope. (Plate VII.) . . 261 



Prof.AV.Grvlls Adams on Measuring Polariscopes. (Plate YIII.) 275 

Dr. 0. J. Lodge on a Systematic Classification of the various 
Forms of Energy 277 

Mr. "W. Baily on a Mode of producing Arago's Eotation. 
(Plates IX.'& X.) 286 

Mr. E. H. M. Bosanquet on the Present State of Experimen- 
tal Acoustics, with Suggestions for the Arrangement of an 
Acoustic Laboratory, and a Sketch of Eesearch 290 

Dr. T. CarneUey on the Influence of Atomic Weight 305 

Prof. F. Eosetti's Experimental Eesearches on the Temperature 
of the Sun 324 

Notices respecting Xew Books : — 

Prof. S. Xewcomb's Eesearches on the Motion of the 
Moon, made at the L'nited States Xaval Observatory, 
Washington 332 

On a Visual Phenomenon and its Explanation, bv William 
AcliToyd, F.I.C. : '. 334 

Precis of a Eeport on Electric-light Experiments, by L. 
Schvrendler, Esq 335 

The True Theory of Fresnel's Literference Phenomena, bv H. 
F. Weber ..'.^ ....!... 339 

An Absorption Hygrometer, by A . van Hasselt 340 


Dr. Carl Barus on the Eelation between the Thermoelectric 
Properties, the Specific Eesistance, and the Hardness of 

Steel. (Plate XI. figs. 1-6) 341 

Dr. T. Carnelley on the Influence of Atomic Weight 368 

Mr. Gr. F. Fitzgerald on the Tension of Vapours near Curved 

Surfaces of their Liquids 3S2 

Dr. S. P. Thompson on the Pseudophone 385 

Dr. W, Spottiswoode on a Mode of Exciting an Induction-coil 390 
Mr. L. Schwendler on a new Standard of Light. (Plate XL 

figs. 7-10.) 392 

Lord Eayleigh's Investigations in Optics, with special refer- 
ence to the Spectroscope 403 

Mr. W. Grant on the Conjugate Positions of two Circular Coils 

of Wire. (Plate XII.) 412 

Notices respecting New Books : — 

Mr. L. Schwendler's Instructions for testing Telegraph- 

Lines and the technical Arrangement of Offices 417 

Proceedings of the Geological Society : — 

Prof. T. M'Kenny Hughes on the Pre-Cambrian Eocks of 

Caernarvon 419 

Messrs. A. Champernowne and W. A. E. Ussher on the 
Structure of the Palaeozoic Districts of West Somerset 419 


Mr. C. T. Clough ou the Whin Sill oi: Teesdale as an x\ssi- 

milator of the surrounding Beds 420 

Prof. T. M'Keuny Hughes on the Silurian Rocks of the 

Valley of the CKvyd 420 

On the Alteration of the Density of Steel by Hardening and 

Tempering, by Carl Froinme 421 

Determinations of the Vapour-Densities, at High Tempera- 
tures, of Substances that attack Mercury, by L. Pfaundler . . 424 


Dr. E. L. Nichols's new Explanation of the Colour of the Sky 425 
Mr. C. C. Hutchinson on the Separation and Estimation of 
Cadmium in the Presence of Zinc : with Remarks upon the 

Separation of Copper, Cadmium, and Zinc 433 

Prof. F. Rosetti's Experimental Researches on the Tempera- 
ture of 'the Sun 438 

Messrs. Guthrie and Boys on Magneto-Electric Induction. 

(Plate XIII.) 449 

Dr. T. Carnelley on the Influence of Atomic Weight 461 

Lord Rayleigh's Investigations in Optics, with special reference 

to the Spectroscope 477 

Prof. H. P. AVeber's Researches on the Elementary Law of 

Hydrodiffusion 487 

On the Specific Heats and Melting-points of divers Refrac- 
tory Metals, by J. Violle 501 

Researches on Daltonism, by J. Mace and W. Nicati 502 

On a new Hygrometer, by Fr. Schwackhofer 503 

On the Galvanic Oxidation of Gold, by M. Berthelot 504 


Prof. S. P. Thompson on the Action of Magnets on Mobile 
Conductors of Currents. (Plate XIV.) 505 

Dr. O. J. Lodge on the Determination of the Variation of the 
Thermal Conductivity of Metals with Temperature, by means 
of the permanent Curve of Temperature along a uniform 
thin Rod heated at one end. (Second Paper.) 510 

Prof. H. F. AVeber's liesearches on the Elementary Law of 
Hydrodiffusion 523 

Prof. F. Rosetti's Experimental Researches on the Tempera- 
ture of the Sun 537 

Mr. R. Hunt on the Influence of the Solar Rays on A^egetation 550 



Mr. "W. C. Eoberts on an Analogy between the Conductivity 
for Heat and the Induction-Balance Effect of Copper-Tin 

Alloys 551 

Dr. O. J. Lodge on a Determination of the Specific Electrical 

Resistance of certain Copper-Tin Alloys 55-i 

Mr. L. Schwendler on a Simple Method of using an insignifi- 
cant Fraction of the main Current produced by a DjTiamo- 

electric Machine, for Telegraph-pui-poses 558 

Notices respecting Xew Books : — 

Eeport on the Administration of the Meteorological De- 
partment of the Government of India, 1877-78 562 

Mr. J. Ebot : Eeport on the Meteorology of India in 

1877, and on the Madras Cyclone of May 1877 562 

Proceedings of the Geological Society : — 

Dr. C. Callaway on the, Pre-Cambrian Eocks of Shrop- 
shire - 564 

Messrs. Jolly and Macdonald-Cameron on a Eemarkable 
and apparently Xew Mineral in the Eocks of Inverness- 
shire 565 

Mr. G. Attwood on South-American Geology 565 

Mr. J. Buckman on the so-called Midford Sands 566 

Mr. E. Wilson on the Physical Geography of the North- 
east of England in Permian and Triassic Times 566 

Mr. J, D. Kendall on the Formation of Eock-basins .... 567 
Mr. S. AUport on the Diorites of the AVai-wick shire Coal- 
field 567 

Mr. C. B. Bro^-n on the Ancient Eiver-deposit of the 

Amazon 567 

Mr. C. Eeid on the Glacial Deposits of Cromer 567 

Mx. H. B. Woodward on a Disturbance of the Chalk at 

Trowse, near Norwich 568 

Mr. T. M. Eeade on a Section of Boulder- clay and Gra- 
vels at Ballygalley Head 569 

Prof. S. Calderon on the Augitic Eocks of the Canary 

Islands 569 

Mr. J. E. Marr on the Cambrian and Silurian Beds of 

the Dee TaUey , 569 

On a Pile with Chloride of Lime, by Alf. Niaudet 570 

On the Abnormal Spectrum of Light, by M. de Klercker, of 

Stockholm 571 

On the Explosion of a Diamond, by Prof. Leidy 572 


I. Illustrative of Dr. F. Auerbach'.s Paper on the Passage of the 
Galvanic Current through Iron. 

II. & III. Illustrative of Frederick Guthrie's Paper on the Fracture of 


IV. Illustrative of Professors Perry and Ayrton's Paper on a neglected 
Principle that may be employed in Earthquake Measurements. 

V. Illustrative of Prof. D. E. Hughes's Paper on an Induction- 
balance and Experimental Researches therewith. 

VI. Illustrative of Mr. W. C. Roberts's Paper on an Examination of 
certain Alloys by the Aid of the Induction-balance. 

VII. Illustrative of Lord Rayleigh's Investigations in Optics, with spe- 
cial reference to the Spectroscope. 

VIII. Illustrative of Prof. W. Grylls Adams's Paper on Measuring Po- 

IX. & X. Illustrative of Mr. W. Rally's Paper on a Mode of producing 

Arago's Rotation. 

XI. Illustrative of Dr. C. Barus's Paper on the Relation between 
the Thermoelectric Properties, the Specific Resistance, and the 
Hardness of Steel ; and Mr. Louis Schwendler's on a new 
Standard of Light. 

XII. Illustrative of Mr. W. Grant's Paper on the Conjugate Positions 
of two Circular Coils of "Wire. 

XIII. Illustrative of Messrs. Guthrie and Boys's Paper on Magneto- 

electric Induction. 

XIV. Illustrative of Prof. S. P. Thompson's Paper on the Action of 

Magnets on Mobile Conductors of Currents. 







JULY 1879. 

I. On the Passage of the Galvanic Current through Iron. 
By Felix Auekbach, Ph.D., of Breslau* . 
[Plate I.] 

THE characteristic enormous value of the specific magne- 
tism of iron is, as investigations accomphshed in the last 
decades have shown, not without influence upon the galvanic 
peculiarities of that metal; for if a current be conducted 
through an iron wire, phenomena make their appearance which 
do not occur with other metals. Some of these phenomena 
shall in the following be submitted to a consideration based on 
new experiments, and judged from a unitarv point of view 
which, I am of opinion, has hitherto been missing in the lite- 
rature of this subject. 

I commence with a brief comparison of the known facts, so 
far as I shall have to refer to them. 

§ 2. (1) The statements respecting ^aZra?2zc co«(iKc^2r27_y vary 
within comparatively "wide limits, even when those which can 
be impugned are excluded. Taking, namely, that of silver as 
equal to 100, the corresponding number for iron was found by 
E. Becquerel (1846), \=12'ob 

Benoitf (1878), 127 

Lenz (1838), 13-1 

Pouillet (1846), 14-1 

Matthiessen (1858), 14-44 

Buft' (1857), 14-77 

Arndtsen (1858), 14-83 

Frick and Muller (1848), 15-9 

* Translated from tlie original Essay (Leipzig, 1878), communicated 
by the Author. 

' t Cvmptes Hendus, t. Ixxvi. p. 342 ; Phil. Mag. [IV.] vol. xlv. p. S14 
(1873), and xlix. p. 78 (1875), 

Phil. Mag. S. 5. Vol. 8. No. 46. July 1879. B 

2 Dr. F. Auerbacli on the Passage of 

(2) T/te conductivity diminishes, or the resistance increases, 
as the temperature rises. If we put 


«V = ""o(l+«i<-/3/-)j 
then is, at all events very nearly, 

ai = a and /3,=/3. 

/3i = in ease /3 = 0. 

Tliis latter relation was found by E. Becquerel, Arndtsen 
(approximately), and Mousson. At the same time 

Becquerel gives a = 0"004726 
Arndtsen . . 0-00413 
Mousson . . 0-004207 

On the contrary, Matthiessen finds /S^ different from ; 

namely, from 

X = X,(l-0-0051182i + 0-000012915^-) 


K-=»'o(l + 0-0051182 «-0-000013281<2)^ 

But here also we can, with very close approximation, regard 
the formula 

w=u'Q(l + at) 

as satisfied. This assumption, namely, leads to the equation 

X = X^(1— «f + aV — ...) 

/ a t"^ \ 


in which [t'] signifies a moan value of t, which can be intro- 
duced, in that term of the correction, in place of the true one. 
It is true that the statements of the observer furnish no cer- 
tain support for this ; but if it be put, in a round number, equal 
to 200° C, we get 

as in fact Matthiossen found (nearly). 

(3) The quantity of heat generated by the current in an 
iron wire is approximately determined by Joule's hnv. I have 
not been able to discover any numbers referring to this more 
accurate than the old ones of Lenz, which, on account of the 
temperature rising with the intensity of the current, are not 





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X. CurreitL-uttensity. 




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the Galvanic Current through Iron. 3 

exactly comparable. The meau values of the times required 
for equal heatings are : — for 

Copper .... 478-9 

German silver . . 4 60 "4 

Platinum . . . . 451-7 

Iron 448-0 

(4) When we close a circuit consisting of a battery and a 
rectilineal iron wire, we observe an extra current in the oppo- 
site direction to thai of the principal current*. At the open- 
ing of the circuit an extra current arises with the same direc- 
tion as the principal current. These currents were discovered 
by Yillari, and were named shock-currents. G. Wiedemann f 
at first based an explanation of them on the assumption of a 
transversal or circular magnetization of the iron wire ; Her- 
wig X and Streintz § have since engaged in a more detailed 
investigation of them. 

(5) Longitudinal magnetizing of iron rods or icires has an in- 
fluence upon their resistance. I mention this point last because 
the results hitherto obtained respecting it have proved most 
anomalous and in part contradictory to one another. Edlund 
and Mousson found no cdteration, Thomson || and Beetz ^ in- 
crease of the resistance ; while even a diminution was inferred 
from older observations, and has recently been confirmed. 
Beetz's results have lately been corroborated by Chwolson** in 
a brief communication. 

§ 3. In the experiments and considerations which I have 
carried out upon the facts here brought together, I started 
directly from the last two points, partly because here the ma- 
terial in hand appeared to me least sufficient for the full un- 
derstanding of the phenomena, partly because I considered 
that I could not concur in the view (in which Beetz and 
Herwig agree) that the cases treated by them (4 and 5) must 
be kept perfectly distinct. Rather have I, with G. Wiede- 
manntt, received from their results the conviction that the 
two phenomena may very well be connected with one another, 
and hence are to he contemplated from a common point of view. 

* The cun-ent made use of for the measurement, passing through the 
iron, I shall constantly in the folio-wing designate as the principal cun'ent. 

t Galvcmismus, 2nd ed. ii. 2, § 743 (1873j. 

X Pogg. Ann. vol. cliii. p. 115 (1874). 

§ Wien. ^er. vol. Ixxyi. (]877). 

II Phil. Trans. 1856, p. 737. 

«i Pogg. Ann. Tol. cxxviii. p. 202 (1866). 
** CarPs Hep. vol. siii. p. 232 (1877). 
tt Gahamsmus, 2nd ed. ii. 1, p. 593. 


4 Dr. F. Auerbach 07i the Passage of 

I commence with the examination of the influence of mag- 
netization uj>on tlio resistance. 

For nu'asurin<r the resistance I used a Wheatstone bridge. 
A universal resistance-box by Siemens furnished the resist- 
ances ivi, W2) w'3 of the three parallel branches. In the expe- 
riments the ratio lOi : tCg was almost constantly as 1000 : 10, 
in some instances as 100 : 10 ; consequently the resistance 
7^3 in the first case represents 100-fold the resistance 10^ to be 
measured. Since O'Ol of a Siemens unit can be measured with 
certainty, the accuracy of the determination extends to the 
fourtli tleciinal place ; it only became uncertain in case w^ 
amounted to more than 10 units. 

I at first used as the measuring-instrument a Wiedemann 
galvanometer with the thinnest of the wire coils that are usu- 
ally joined to it, afterwards one constructed by Sauerwald 
according to Magnus' plan. By means of mirror-reading I 
could estimate with certainty 0*1 of a scale-division ( = 0'1 
millim.). The last-mentioned instrument is highly suitable 
for investigations in which rapidity of observation is import- 
ant, on account of the quick suppression of the vibrations. 

The first and most difficult problem was, hoio to exclude the 
influence of variations of temperature ; for when we consider 
that according to the statements of Thomson, Beetz, and 
Chwolson the upper limit of the alterations of resistance by 
magnetizing is given by the ratio 1 : 1000, and that an alte- 
ration of resistance corresponding to this limit value is pro- 
duced in iron by a change of temperature of 0°*2 C, it is evi- 
dent what careful attention ought to be directed to this point. 
The effects of temperature can either be set aside by a suitable 
arrangement of the experiment before the commencement of 
the observations, or eliminated by calculation after their con- 
clusion. In regard to that portion of those influences which 
is produced by the principal current itself, after some prelimi- 
nary experiments I decided for the latter. Of course, in the 
equation of the Wheatstone bridge, I could easily have made 
the ratio w^ : lo^ independent of the temperature by having 
the resistance ic^ for the most part of iron, and taking only the 
small part requisite for the actual regulation out of the resist- 
ance-box. But since the ratio iC2 : ?t'i was = 1 : 100, iron 
wires of considerable length would have been necessary, which 
for other reasons I was obliged to avoid. Moreover the heat- 
ing produce 1 by from 1 to 3 Danicill elements, such as I used 
for the principal current, during the mostly very short time 
that the current was closed, was extremely little ; and it is 
well known that with small values of the foreign influences (of 

the Galvanic Current through Iron. 5 

whatever kind they may be) elimination furnishes very reli- 
able results. Thereby the scheme of all the experiments which 
I made assumed the form ay — h—a2, where a-^ signifies the 
experiment before the magnetization, h the same after magne- 
tizing, and ^2 after demagnetizing. The results h and ^ ^ 

are then fairly comparable if the difference a^—a^ is small. 

A second portion of the temperature-influences, that occa- 
sioned by the surroundings, can also be reduced to a minimum, 
and that minimum eliminated. The latter can here be done 
with peculiar facility, since the periods of the extreme varia- 
tions of temperature stand in no connexion whatever Avith 
those of the alterations of the resistance conditioned by the 

There still remains for discussion the third and most import- 
ant part of the influences of temperature, namely those condi- 
tioned by the magnetizing-arrangement. This in the beginning 
consisted of a spiral of thick wire, spun over and waxed, and 
wound upon a glass tube, through which the magnetizing 
current flowed. The iron wire was pushed into the glass tube, 
and the entire apparatus set up at a distance of several metres 
from the galvanometer ; so that neither the magnetism nor 
even the magnetizing current acted directly upon the galva- 
nometer. It nevertheless appeared that the heating action of 
the magnetizing current was conveyed by radiation from the 
spiral to the iron wire and occasioned variations in its resist- 
ance, which, partly by their considerable amount, and partly 
because the periods of both variations are identical, concealed 
all the alterations which were to be measured*. Hence it 
was important to construct an adiathermanous magnetizing- 
apparatus. In this I succeeded by making use of the proce- 
dure often employed by Joule in his thermal investigations — 
namely, placing in layers one over another a number of series, 
each consisting of an adiathermanous, a badly conducting 
material, and a material of great heat-capacity. The copper 
spiral was accordingly wound upon a wide glass tube, this 
drawn over a thick-walled caoutchouc hose ; inside this a nar- 
rower glass tube was inserted, and in the latter the iron wire, 
mostly wrapped round with paper. To carry out the principle 
completely I should have had to put between the narrower 
glass tube and the iron wire a layer of substance of great heat- 
capacity — for example, a stationaiy stream of alcohol or melt- 

* These variations of resistance furnish a very serviceable method of 
following the temperature in a galvanic battery. I intend to return to 
this subject in another place. 

^ Dr. r. Auerbacli on the Passage of 

jng ice. Eccently, however, experiments have been made on 
dielectric, diama^netic, and electrolytic influences of such 
surrounding liquids, which appeared to me in the present case 
not to be neglected ; and an apparatus so constructed was 
sulficient for two of the magnetizing forces which I used — a 
Daniell and a Bunsen battery of five cells at the most. With 
the third (the current of a Granune machine driven by a 
steam-engine), it is true that in most cases sensible thermal 
effects still remained ; they were, however, small enough to 
admit of elimination. The employment of such powerful 
magnetizing forces may perhaps in general appear to be su- 
perfluous, since it is usually assumed that iron would be mag- 
netized to so-called saturation by much feebler forces. But I 
should doubt whether in such cases it is actually attained ; it 
is probably " nearly " reached*. Perhaps the molecular mag- 
nets deviate, in the mean, only a fraction of a degree from the 
axis of magnetization ; but just the influence of the still pos- 
sible twist may, in reference to such questions as these hereto 
be exammed, be material. 

"With the arrangement adopted there was no fear of thermo- 
currents ; but it was necessary to reduce as much as possible 
the intensity of the above-mentioned extra currents. The ne- 
cessity of this will not, perhaps, be at once obvious. In the 
present investigation, however, lasting influences are in ques- 
tion ; and from these those momentary phenomena must be 
easily distinguishable. But, in the first place, it is for many 
reasons desirable to be able to determine also these lasting in- 
fluences immediately after the closing of the current, in order 
that it may soon be opened again ; and, secondly, those extra 
currents are any thing but momentary phenomena. I have 
much rather found that here the phenomena known under 
the name of after-effect play a great part. This is the more 
disagreeable, as the still remaining temperature-influences 
continue to operate according to the time occupied by the 
radiation and conduction. I have, on this account, operated 
throughout with iron wires, in which Yillari's currents appear 
far less intense than in rods. 

§ 4. It is a priori to be expected that the nature of the ynvQ 
(whether it consists of steel or iron, whether it is hard or soft, 
&c.) will have some influence on the phenomena exhibited by 
it, that a wire which has not yet been galvanically operated on 
behaves dift\,'reutly from one through which, during a longer 
or shorter time, currents have passed, or which has already 
repeatedly undergone longitudinal or transverse magnetiza- 
tion. But to this must be added an essential moment, con- 
• Thus M. Beetz cautiously expresses liimself. 

the Galvanic Cxirrent through Iron. 7 

sisting in the ratio of the intensities of the magnetizing and 
the principal current, and to which I shall further on attach 
uiv theoretic considerations. From these causes the numbers 
of the following Tables show great diversitv. 

Of the series of experiments with weak magnetizing cur- 
rents, some are already serviceable before the iniproyement of 
the magnetizing-apparatus. I denote by: — H the electromo- 
tiv^e force generating the principal current, M that producing 
the magnetizing current; D the electromotive force of a Da- 
niell, B that of a Bunsen element ; n the number of turns of 
the magnetizing spiral ; I the approximate length, d the thick- 
ness, of the iron or steel wire ; lo^ the resistance of the same, 
measured in Siemens units, for M = 0, iv the same for M > ; 
w^ the resistance of the copper conducting-wires to the resist- 

ance-box ; S the quotient ; t the time occupied by the 


Passing over the time-details of the phenomena, I first give 
only the numbers hereto belonging. 

1. H = M = 1D; ?i = 106; (annealed iron wire /\) 
d = about 0'5 millim. 

Wq + iv^ w + iVj^ iCq + ivj^ (it'j = 0-5209) 

1-0300 1-0296 1-0304 S= -0-0012. 

2. H, M, 71, as before, /i. 
Wq + Wj^ iv + Wf^ icq + iOj^ (?(j^=0-5211) 
1-0304 1-0294 1-0302 S= -0-0018- 

3. H, M, n as before. (Annealed iron wire/g) d about 
0-5 millim. 

Wq + Wj^ w + w^ u'q + Wj^ (w7^= 0-5210) 

1-7478 1-7459 1-7476 S= -0-0015. 

4. H and M as before ; 9i = 166. Wire/i. 

Wq + zCj^ lo + ic^ ^ro + ^Cl^ {u\ = 0-5201) 

1-0227 1-0216 1-0229 S= -0-0024. 

Mean of 1-3, S= -0-0015, while in 4 S= -0-0024. 

The magnetizing force is proportional to n : according to 
the abo"se, therefore, 8 is proportional to the magnetizing 
force. According to its sign, 8 is negative. The length of 
the wire (experiment 3) appears to be without influence. 

* Unfortimateh', in most of the older experiments some of these data 
are wanting, it not having been anticipated that they -would he required. 

8 Dr. F. Auerbach on the Passage of 

5. H = 3 D ; M = 1 D. Wire J\. n = 106. The magneti- 
zing current remained closed for an hour. 

«'o + «v= 1-7429 iu + ir^= 1-7 S26 w^ + w^=l-7SSQ 

(iv,, =0-5207) ; therefore S= -00068. 

Here, therefore, first a greater transient, secondly a perma- 
nent diminution of the resistance took place, although there 
was no demonstrable permanent magnetization. Tlio tempo- 
rary diminution becomes still greater, if in its calculation wo 
neglect the permanent — that is, in calculating the ditferenco 
w—zCq, keep in view only the initial zcq. Then we have 

8^= -00084. 

6. H=5D; M = 1D; n = 106. Wire/j. 

wJo + u'^= 1-7366 ic-\-tCi^= 1-7 1S9 w'o + ?r;^= 1*7299 
(w^=0'5210); therefore S= -00159. 
Neglecting the permanent alteration, we get 
§1= -00186. 

Here the temporary alteration of the resistance is still 
greater, its value reaching nearly 2 per cent. But the per- 
manent alteration is also greater than in the preceding case. 

Some series of experiments on unannealed iron wires ex- 
hibit the same phenomena, only more feebly. On the con- 
trary, \\ith a thin unannealed steel wire the resistance dimi- 
nished nearly 3 per cent, when H = 3B, M=1D were chosen. 

Most of the experiments made before the improvement of 
the electromagnet, however, show an increase of the resistance 
with magnetization, and, indeed, a greater temporary and a 
smaller residual increase. As, however, in them it is hardly 
possible to separate the influence of the increase of tempera- 
ture, I have, with the exception of a few apparently reliable 
ones, made no use of those experiments. 

7. I will next mention two experiments with thin unan- 
nealed iron wires, in which no alteration amounting to 0-0002 
per unit of the resistance occurred. In both was H = 2D, 
71 = 92 ; further, in one of them M = 3D, in the other M = 2B. 

8. Annealed iron wire /a {d about =0-6). H = 1D ; M = 3D ; 
n = 92. The resistance of the conduction- wires is already de- 

w?o=0-52.13 10 = 0-5234: zro=0'5214 S= +0-0038. 

9. Experiment 8 several times repeated. 
2^0=0-5214 26'=0-5232 u-o=0-52U 8= -f 0-0035. 

tlie Galvanic Current through Iron. 9 

The influence of the repetition many times of the same ex- 
periment rarely showed itself so insignificant as in this case. 

10. Instead of the resistance-box, a rectilineal rheostat was 

employed. The numbers for u'q and lo are expressed in terms 

of an 'arbitrary unit. H=1D; M = 2D ; ?i=92. Mean 

values : — 

M = 6019-81 r 1 _lq^ 

•- "J V ht'— w'oJ= +3-4, 

[r^'] =6023-2/ ^ ^ 

1 00000 -?<'o 


10. 100000 -«; 

1= +0-00135. 

The total resistance of the rheostat is put equal to 100000 ; 
the aboye calculation was necessary, because here equilibrium 
was restored by shifting a binding-screw. 

11. In experiment 10 the principal current passed in the 
iron wire from the south to the north pole. The principal 
current was now sent through in the opposite direction. The 
mean yalues found were : — 

[w'o] = 6021; [ic'] = mU; [to-ic^-\= +^; S= +0-00122. 

(According to the same reckoning as aboye.) Here, how- 
ever, it must be noted, first, that the iron -wire with which 
these two series of experiments were made had already been 
repeatedly passed through by the current, and, secondly, that, 
in the calculation of the mean values in 11, the first numbers, 
deviating, were left out of the account. The complete series, 
namely, are as follows: — 


therefore w constantly > iv^. 


= 6019 >| 


= 6024 


= 6021 


= 6023 


= 6019 " 


= 6022 


= 6020 


= 6024 J 



= 6022 


= 6020 


= 6022 1 


= 6025 1 


= 6022 


= 6024 


= 6020 


= 6023 


= 6020 J 

to < W'o 

r-iv > iOq 

The reversal of the direction of the current in the iron has 

10 Dr. F. Auerbach o/i the Passage of 

therefore for its consequence a momentary but no permanent 
change of sign of h. That the repeated opening and closing 
of the magnetizing current exercised no influence depended 
probably on stationary relations having already entered, in con- 
sequence of the wire having been long in use. In order to 
test this sup])osition I gave to a yet unused iron wire of like 
constitution the same dimensions, and obtained: — 

12. [u'o] = 6018 6020 6017 6015 6013 
[^c^= 6011 6011 6008 6006 

Means:— [u»o] = 6016-6; [»'] =6009-0; [_w-w^'\ = -l-^]; 

S= -0*0032. 

Here, therefore, S is negative. In fact, after I had closed 
and opened the magnetizing current about 100 times, the ab- 
solute value of S diminished, and on the next day I obtained, 
as in 10 and 11, a small positive value of h. But I have only 
observed such change of sign of S when, for ?? = 92, the ratio 
H : M = l : 2 or did not much difl^'er from this. Only when 
very intense currents had passed through the wire for a longer 
time, or when I had repeatedly reversed the direction of the 
magnetization, did the results become in other pases also and 
completely irregular. 

Shortly before the construction of the adiathermanous ap- 
paratus, I made some more experiments, in which, it is true, 
I veritied an influence of the heating ; but I believed I should 
be able to eliminate it by comparison with experiments on 
copper wires. The specific heats, namely, of iron and copper 
are to one another about as 7 : 6 ; and, according to Benoit, 
their temperature-coefticients « are approximately in the same 
ratio for the galvanic resistance. If, then, we employ the 
same value of M and the same magnetizing-apparatus, and 
give to the surfaces of the iron and the copper wire equal mag- 
nitude, by which also their volume becomes the same, we get 
in both nearly equal augmentations of resistance by radiation 
from the magnetizing-apparatus. Hence I proceeded in the 
way indicated, and obtained (the indices /and c refer to the 
soft-iron and the copper wire respectivelv) : — 

13. Resistance-box. H=1D; M = 2B; ?i = 73. 

8^=0-0023 S/= 0-0042 
8^-a,= S= +0*0019. 

14. The same repeated. 

S^=0-0026 S/=0-0039 5= +0*0013. 

15. H = 1D; M = 3B: n = 73, thicker wires. 

8^=0-0017 S^=0-0044 8= +0*0027. 

the Galvanic Current through Iron. 11 

Here S has increased, in comparison with experiment 13, 
exactly in the ratio of the magnetizing force. 

The following series of experiments were all made with the 
adiathermanous apparatus. 

With unaunealed iron wires the residual eflPect of the extra 
currents after the closing of the magnetizing and the principal 
current is very protracted; so that here we can often only 
with difficulty separate the transient from the permanent phe- 
nomena. Hence I designate by ii\ the resistance in the first 
period (often amounting to some minutes) after the closing of 
both currents, bv u'o the resistance that has become constant. 

16. H = 1D;'' M = 3B; 71=150. Iron wire /^ {d about 
0*60). Mean values : — 

u\ + 

^"« = !]'^[!?;^^1 -.=0-0698 
:::=0:79J52 ---o=0;00061 
w,=o-imu] "•2-«'o=0-00007 


ic<, — u\ 

= §2= +0-00010. 


17. The same repeated. 

w'o= 0-78998^ 

u\ + 

2Pi=0-79050 I «-i-?ro=0-00052 
M-2=0-79010 I w2-u-o= 0-00012 

it'o=0-78998 ) 

Si = 0'00072 
82 = 0-00016. 

Therefore, on the repetition of the experiment, S^ has become 
less, 82 lias increased. With this agrees the fact that after 
being used many times wires mostly give no perceptible dif- 
ference between h^ and So. 

18. H = 1D; M = 3B.' Strong iron wire/5 (fZ about 1-3). 

J M'i= 0-16610 tci-«-o= 0-00024 
^^'* '^ \ «-2 = 0-1 6630 f w2-ito= 0-00016 

Si = 0-00260 82 = 0-00156. 

Here not only are S^ and h^ absolutely greater than in the 
two preceding series, but 82 is much greater in comparison 
with 81. There only one fifth part of the initial increase of 
resistance was permanent; here, more than half. 

12 Dr. F. Auerbach on the Passage of 

19. Strong iron wire, annealed, /g. H=1D; M = 4B; 
71 = 212. Mean values. 

tvQ=0-b02d ?c=0-5171 ioq=0-o07S 

8 = 00240. 

Permanent increase A = 0*009 7. If we neglect this, we got 
for the transient increase 

5 = 00281. 

These values are extraordinarily high. The permanent in- 
crease of the resistance can also be inferred fi'omthe fact that 
we have here to do with a])normal proportions. Of course 
this conclusion must, to a certain extent, be extended to the 
following series of experiments, based upon another wire. 

20. H and M as in 19. A thin iron wire, annealed, /;, 
several times operated on galvanically; d=0'liK 

7^0 = 6-3549 w = 6-4532 w^^QSQU 

S= +00147. 

Further, with the same signification as above, we get 

A = 0-0015 and Si = 00156. 

The disproportionately low value of A, compared with that 
found in 19, can be accounted for from the circumstance that 
the wire/; had already, in consequence of having been fre- 
quently passed through by the current, considerably neared 
its stationary condition. 

21. H = 2D; M = 3B. A thin hard iron wire /g ; d=0-15. 

w.Q + »i^ = 11-0142. 

No alteration of resistance, not even O'OOOl, although here, 
in spite of the very slight thickness, the extra currents corre- 
sponded to a considerable increase of resistance for the moment 
of the closing of the current. 

22. H = 2D; M=1D; n = 92. Hardiron wire /;; 1=1670, 

tro= 7-3961 u'= 7-3903 «'„= 7-3973 

S= -00009. 

The same wire, however, showed after longer working, after 
8 had constantly approached nearer and nearer to zero, at last 
small positive values of 8. In the meantime it was submitted 
to experiment 23. 

23. H = 1D; M=2D. Wire/g. 

i<Jo= 7-3991 z(;= 7-3997 «'o= 7-3993 
S= -00002. 

the Galvanic Current through Iron. 13 

24. Eepetition of 22. As mentioned, it gave an augmen- 
tation, though hardly sensible, of xi\. For a control I pro- 
duced, out of the same coil of wire from Avhich j\ had been 
taken, a new wire of the same dimensions, nearly, and found 
for H = 2D, M=1D (therefore as in 22):— 

1^0=7-3608 u'= 7-3559 1^0=7-3602 

8= -00006, 

therefore a negative value of S, as in 22. 

25. In experiment-series 6 and 21 the conclusion was reached 
that the resistance of hard iron •v^'ires was not changed by 
maffuetizing them. I sought to realize the same case with a 
tempered thick steel wire Fi (Z= 1450, d= 1-31). I succeeded, 
■when H was =2D and n = 92, with almost equal approxima- 
tion when M was = 2D and M = 3D. This point can be fixed 
still more exactly with annealed iron A^res. On the contrary, 
in hard steel wires there was always an alteration of the resist- 
ance; and, indeed, with H constant, the more insignificant 
the magnetizing force the smaller in general was the altera- 
tion. Of the experiments w^ith slight magnetizings I will only 
mention that they mostly ;\nelded lower values of S than those 
with iron wires ; only with the lowest values of the ratio M?r : H 
does the opposite take place. On the other hand, I will give 
some more series of experiments with magnetizing forces to 
w^hich, in iron and tempered steel, positive values of 8 would 
have corresponded. 

26. H=1D; M = 3B; 7i=110. Wire F3 of English steel 
(music-steel). Z=1280; o?=0-91. Mean values (the first 
experiments being excluded): — 

, rwv = 0-400911 Annmo 

(zr^= 0-050 nearly). 
g= -000034. 

If now the magnetizing current was reversed, there followed, 
as at the commencement of the first series, first an increase of 
h by magnetizing, which, however, after the current had 
passed twice had already given place to a diminution. Gene- 
rally, this wire proved very favourable, not only for these 
measurements, but also for those of which I have yet to speak 
in the course of this investigation. But the absolute values 
of 8 are here much smaller than in other wires; already on the 
25th May, with a series (M) of 5B, I had obtained scarcely 
higher values of S. 

In order to determine whether the cause of this w^as the 

14 Dr. F. Auerbacb on the Passage of 

sliirht dependence of the resistance on the magnetization of 
the En^rlish steel, or wlietber considenihl}' stronger magneti- 
zing I'orces were not required here in order to produce, even 
approximately only, the state of so-called saturation, I made 
use of a Granmie machine of the newer construction (1875), 
a short time previously acquired for this laboratory bv Trof. 
0. E. Meyer, and, driven by a steam-engine, ca})able of ope- 
rating with considerable effect. Its distance from the galva- 
nometer amounted to about 25 metres ; the electromagnet 
was set up between the two, at the distance of 5 metres from 
the machine, and 20 from the galvanometer, and connected in 
both directions by thick copper wires. The spiral never grew 
so hot that it could not be touched with impunity. The caout- 
chouc pipe never exhibited any trace of heating, even with the 
most rapid rotation of the machine (1200 revolutions per 
minute). Notwithstanding, many of the series of experi- 
ments made with soft iron wires, especially with thin ones, 
proceeded in a manner which I can only account for by influ- 
ences of temperature. If we seek to eliminate these, we ob- 
tain increases of resistance by magnetization rising to 1 per 
cent, and over. Simpler and more reliable are the results of 
the experiments with steel wires, the mean values of which 
are here extracted : — 

27. H = 1D; M = Gramme machine (number of revolu- 
tions,j9 = 700); 7i=110. Thin steel wire F^, Z=2000, d = 0-21. 

w'o=8-4960 u'=8-4803 S= -00019. 

28. The same repeated (4 series of experiments). 

w7o=8-G415 ^t; = 8-6346 S=-0'0008. 

29. Steel wire F3. H=1D; M= Gr. machine (p = SOO). 
wjo=0-3435 u' = 0-3419 2ro=0-3435 S= -00047. 

30. To this experiment was joined immediately a control 
experiment with a copper ware. (Such control experiments 
were also previously made from time to time.) H=1D; 
M= Gr. machine (7^ = 1000-1200); /=2220; d = OuO. Mean 
values : — 

iro=0-14138 rr = 0-14149 m'o = 0-14144 S=+0'00056. 

For copper Avi re, therefore, S is, first, positive, and, secondly, 
much smaller in absolute value than in 29, although p is much 
greater. Besides, all the other experiments with copper wires 
have yielded considerably lower values still of 8. If these 
alterations of resistance should prove to be connected with the 
magnetic behaviour of copper, they will disprove the generality 

the Galvanic Current through Iron. 


of the diminution of resistance observed by Schuster and 
Stewart* on a magnetized copper v.'ire. 

31. The following series of experiments serves to show that 
the influence of the magnetizino- is demonstrable even when 
accompanied by considerable influences of temperature. On 
making certain simplifying assumptions, it is easy to ascer- 
tain the law according to which the resistance in the circuit of 
the principal current changes with the time through lateral 
radiation of the spiral. If now, in addition to this, we carry 
out a longer series of alternate determinations of u-q and ic, and 
note in each the time t, we obtain by the numbers Wq the con- 
stants of that law. If we then construct the curve represent- 
ing the law (it is in general a transcendental) and compare it 
with the curve deduced from observations, we find diflerent 
ordinates for the abscissae corresponding to the times of the 
determination of the quantities w. These difterences refer to 
the magnetization. I give a series of experiments of this kind 
with the Gramme machine and the wire F3 ; w^, u\, iC2 are the 
resistances for p = 0, }) = 4:00, and/) = 800. 








h m 

2 50 


3 7 


















ti', — Wg 

34 0-3416 1 

1 1 

- 0-0035 


u--, — u\ 

■■ Si we find, according to the above, three values 

of ascending magnitude, for So one only, namely : — 
S,= -0-0015, -0-0021, -0-0030; 

therefore, mean, 

§,= -0-0022; and So =-0-0106. 

It is of course presupposed here that the discontinuities pro- 
duced by the variation of j) are masked by the residual thermal 

The value of S<j here should agree with the value of S in 29; 
for H, M, n have the same values. But it is more than double 

* Phil. Mag. [4] xlviii. p. c3o (1874) ; Pogg. Ann. cliii. p. 205. 

16 Dr. F. Aucrbach on the Passage of 

as great. Fi tr. 1 (PI. I.) gives a part of the observed and the 
calculated curves. 

§ 5. Hand in band with the oxperimcnts on the influence 
of magnetization went experiments on the extra currents lohich 
are generated hy every current in iron. I forbear to communi- 
cate these experiments in detail, since in their essential results 
the}' agree with those of MM. Herwig and Streintz. Quanti- 
tative statements, however, on the intensity of the extra cur- 
rents, in any comparable measure, on the part of the latter 
observer we have none ; and Herwig only states that once a 
diminution of the resistance of 0*001 1 to 0'0014 would have 
corresponded to the deflection of the galvanometer-needle ob- 
tained after the opening of the principal current, if the cur- 
rent had persisted. As in general I took no account of an 
agitation of the wires, I mostly obtained extra currents of 
longer duration, by which I attained the possibility of some- 
times carrying out very exact resistance-measurements of the 
above sort. The values which I obtained are, in part, by no 
means inconsiderably higher than Herwig's above mentioned. 
The signs of these values were, with few exceptions (to be 
explained by extraneous influences) constantly such as to show 
that on the closing of the principal current the standard resist- 
ance must have been heightened, ivhile on its opening that resist- 
ance must have become less. Further, I find (as Herwig did) 
the deflections with steel less than with iro7i; but if I follow up 
the rate of each (which with iron, especially annealed wires, 
is much quicker than with steel), I find for the integral cur- 
rents corresponding to the deflections values not essentially 

Now I obtained far more intense extra currents ichen I led 
the current through magnetized iron or steel wires, although 
their direction was constantly the same as if the wire had not 
been magnetic. In those cases in which the definitive resist- 
ance was increased by magnetizing, a still greater resistance 
always corresponded to the extra current. Tliis made itself 
recognizable by a deflection towards the side of the greater 
resistances, following after the bridge had been equalized for 
the unmaguetic condition of the wire, which deflection was 
greater than had corresponded to the permanent deviation of 
the needle ; and this latter also, after the oscillations of the 
needle had long ceased, diminished, in most cases slowly, a 
little more, till it took the value given in the Tables of § 4. 
But even in those cases in which the resistance in the mag- 
netic state was less, the deflection constantly took place first 
toward the side of the greater resistances. I do not give nu- 
merical data, because a similar diversity prevails as in the 

the Galvanic Current through Iron. 17 

numbers of § 4. The intensity of the extra currents increases 
with the amount of the maQ-netizina force, at the commence- 
ment more quickly, afterwards (/. e. with high magnetiziugs) 
more slowly than it. 

It is here presupposed that the principal current is not closed 
till some time after the closino; of the ma£netiziuor one. If it be 
closed shortly after or simultaneously with that current, the 
phenomena become very irregular. They are totally changed 
Avhen the principal current is closed first, and then the mag- 
netizing one. The closing-currents are then feebler by far ; 
but if accessible to observation, their direction is found to be 
the opposite ; that is, they correspond to a diminution of re- 
sistance. Sometimes a whole series of oscillating extra cur- 
rents is observed. 

§ 6. The experiments communicated in § 4 appear to me 
adapted to mediate between the results obtained by previous 
observers relating to this subject. Indeed nearly all of these, 
however divergent they may seem, reappear in my results, 
and receive their provisional explanation by the variety o'f the 
circumstances under which they were gained. Beetz found 
under all circumstances an increase of the resistance ; but he 
appears to have always employed very powerful magnetizinor 
forces, and to have operated only with iron and not with steel 
rods ; and under these two conditions I also constantly ob- 
tained positive values of S. Stewart and Schuster observed 
in a magnetized copper wire, when the magnetizing force was 
great, a diminution of the resistance ; it behaved, then, like 
my steel wires. Unfortunately, it is not stated whether the 
wire consisted of pure (diamagnetic) copper or of copper con- 
taining iron (paramagnetic), as commercial copper usually 
does. Edlund and ^Jousson did not get any alteration of the 
resistance by magnetizing, although the accuracy of their 
measurements was not essentially interior to that of Thomson^'s. 
In my Tables also some are found vrhich give for h the value 0. 
Lastly, Adams published in the ' Proceedings of the Roval 
Society ' * a preliminary communication from H. Tomlinson 
(but I have in vain sought the full paper in the ' Transac- 
tions^). According to these data, which afford extremely 
few fixed points, in hard steel the magnetizing has for its con- 
sequence a diminution, in iron and soft steel an increase of the 
resistance. This is in complete accordance with my state- 
ments, if it be admitted that the magnetization applied by 
Tomlinson was always considerable. This is probable from 
the enormous magnitude of the numbers which I desio^natG 

* June 17, 1875. 
Phil. Mag. S. 5. Yol. 8. No. 46. July 1879. 

18 Prof. Thompson and Dr. Lodge on Unilateral 

by h. My values lie between the limits 

-O-OlSGand +0-0281*; 
Tomlinson's values between 

-O-Ofi +0-04 (?). 

Subjoiniiio- the liniithig value from the experiments of Beetz, 

+ 0-0000, 

with which Chwolson's exactly, and Thomson's in some mea- 
sure, agree, we see that my numbers hold the middle place. 

Tomlinson moreover a])pears to have carried out the mag- 
netizings while the principal current Avas closed. I have men- 
tioned that in such cases an extra current arises, corresponding 
to a diminution of the resistance. Now, since these extra 
currents in hard steel often pass very slowly, perhaps a part 
of the G per cent, decrease might result from this, and of the 
1-4 per cent, increase in soft wires we might deduct a part 
for the heating acknowledged bv Tomlinson himself. 
[To be continued.] 

II. On Unilateral Conductivity in Tourmaline Cri/stah. 
Bi/ Professor S. P. Thompson and Dr. 0. J. Lodgej. 

IN thinking of the possible physical conditions of structure 
•which might permit an explanation of the phenomena of 
pyroelectricity of the tourmaline and other crystals, an hypo- 
thesis suggested itself independently to each of the present 
writers. At the Glasgow Meeting of the Association in 187G, 
a paper was read by the second-named of them, upon a Me- 
chanical Model illustrating the phenomena of electric curreuts|. 
The physical illustrations there given of the relation of elec- 
tromotive force and resistance to the particles of matter in a 
conducting circuit led the way to the suggestion that the in- 
ternal polarization of each particle of the crystal, which had 
been assumed by Sir William Thomson as a sufficient cause of 
the phenomena of pyroelectricity, might become explicable if 
it could be shown that such bodies as possessed pyroelectric 
properties possessed also a unilateral conductivity for elec- 

The term unilateral conductivity is defined as follows: — Let 
a certain direction from a point A to a point B in a homoge- 
neous substance be considered. Then if it is found that the 

♦ The value — 0-03 has been given by only one experiment -with a steel 
wire, M« : II being very small and the absolute value of II very great. 

t Read before Section A of the British Association at Dublin, Septem- 
ber 1878. Communicated bv the Authors. 

I See Pbil. Mag. Nov. and Dec. Suppl. 1876. 

Conduct ivitij in Tourmaline Crystals. 19 

resistance to the passage of electricit j (or heat) is greater or 
less when the flow is in the sense AB than it is when in 
the sense BA, such a substance possesses a unilateral con- 
ductivity for electricity (or heat, as the case may be) in the 
given direction. Some apparent cases of unilateral conducti- 
vity for electricity had been described by Dr. A. Schuster 
(vide Brit. Assoc. Eep. 1874). It was to be expected that a 
phenomenon of unequal heating, the analogue of the unequal 
electrification of the tourmaline when warmed, would be found. 
It was also imagined, by a reversal of the known pheno- 
mena of pyroelectricity, that a pyroelectric crystal when elec- 
trified from without might have its ends unequally warmed. 
If the development of opposite electrical states at the two 
ends, and the establishment of a difference of potential between 
them, were a result of a unilateral conductivity, all the ana- 
logies of the conduction of heat and electricity pointed to the 
probability that the tourmaline would be found to possess a 
unilateral conductivity for heat also. 

The first named of the authors, therefore, proposed the fol- 
lowing experiment. Let a slice be cut from a tourmaline 
crystal having its two faces principal planes of section of 
the crystal, and therefore containing the crystallographic, 
optic, and pyroelectric axis. Let the slice be covered with 
wax, and let it be warmed by a hot wire inserted in a central, 
hole after the method of Do Scnarmont. The tourmaline we 
know to be a negative uniaxial crystal ; and the isothermal 
line marked out by the melting of the wax will be an ellipse 
having its minor axis along the crystallographic (and optic 
and pyroelectric) axis. If the crystal, however, possess uni- 
lateral conductivity for heat, the isothermal lines will be no 
longer symmetrical about the point of application of heat, but 
will be displaced along the crystallographic (and optic and 
pyroelectric) axis toward one extremity. We therefore, as a 
preliminary trial, procured such a slice of tourmaline (which 
we Avill call tourmaline "A") from Mr. Ahrens. It .was 
roughly circular, of about 2 millims. thickness, and measured 
along the axis 25*3 millims., across 25"6 millims. Experi- 
ment proved that when the point of a hot silver wire was in- 
troduced into the central hole, the isothermal line bounding 
the melted area possessed the form of a distorted ellipse, 
always displaced toward the analogous pole of the crvstal. 
Two series of measurements were made : — one, of the areas 
marked out by the melting of the wax; the other, using Meu- 
sel's double iodide of copper and mercury, which changes at 
94° {circa) to a black tint. This method gave isothermals 
of a higher temperature than the wax. The extremities of 


20 Prof. Thompson and Dr. Lodge on Unilateral 

the minor axis -wore scratched witli a needle npon the surface, 
and afterwards measured. The following is the series of mea- 
surements made : — 

Crystal " A." 
Measurements of Semiaxes minor of Isothermal Curves. 
Series 1. (Wax.) 
. Semiaxis — , Seuiiaxis +. 

{a) 2-5 3-1 or 100 : 124 

{b) 3-1 4-4 100 : 142 

(c) 4-3 5-9 100 : 137 

(d) 5-6 7-2 100 : 129 

{e) G-7 8-4 100 : 124 

(/•) 10 12-8 100 : 128 

Series 2. (Double Iodide of Cu and Hg.) 

{g) 2-0 2-5 or 100 : 125 

(h) 3-1 4-2 100 : 135 

li) 3-9 5-1 100 : 130 

\h) 5-9 6-9 100 : 117 

Mean 100 : 129-1 

These results differ some\Yhat widely from the mean figure ; 
yet it is significant that they all tend in the same direction. 
It is to he remarked that in all cases these experiments were 
made quicMy, and that in no one case was a condition of 
thermal equilibrium established in the crystal between the 
central gain of heat and the loss by radiation &c. on the outer 
edges. The result then appeared to be that in a crystal icJiich 
teas getting tcarmer the heat flowed more easily towards the 
analogous pole than away from it. 

It is clear that the isothermal curve produced thus will 
be one possessing geometrical discontinuity ; for the resolved 
parts of the radii from the centre of heating parallel to the 
axis will on one side of the centre be lengthened, and on the 
other side reduced, in a ratio dependent on the unilateral co- 
efficient of conductivity. Hence the curve will consist of two 
semiellipscs having a common major axis, but having ditferent 
semi- minor axes in the ratio given above, viz. on the average 
1-3. These results were obtained in July 1877. They were 
not published at the time, because it was desired to obtain 
further confirmation with other specimens of tourmaline. No 
suitable specimens, however, could be met with ; and the mat- 
ter rested at this point for some months*. 

* Another tourmaline, a transparent green crystal, obtained frora Lau- 
rent of Paris, has since afForded equally significant results — the isother- 

Conductivity in Tourmaline Crystals. 21 

It then occurred to the authors that it would be worth while 
to measure the flux of heat and of electricity across a thin 
wall of tourmaline, the crystal being cut for that purpose at 
right angles to its crystallographic axis. For some months 
no suitable crystal could be obtained ; but eyentually, by the 
kindness of Professor N. Story Maskelyne, this difficulty was 
removed, and a slice of opaque black tourmaline from the 
Ural Mountains, which we will speak of as tourmaline "_B," 
was placed at our disposal. Its dimensions were 35-5 milUras. 
length by 24-4 millims. width; and it varied in thickness from 
2*5 to 2-14 millims. 

Two methods of measuring the flow of heat through such a 
slice were suggested. One method, applicable only to a slice 
at a constant temperature, is described, and the mathematical 
solution of the case is given, in the Philosophical Magazine 
for February 1878, by the second-named of the authors, under 
the title " On a Method of Measuring the Absolute Thermal 
Conductivities of Crystals " &c. The opportunity of applying 
this method to the tourmaline has not, however, arrived. ^ 

A second and simpler method of experimenting, and giving 
results of qualitative value only, was suggested and carried 
out by the first-named author. It involves the use of a 
sort of reversible contact-thermometer. The crystal-slice 
was fixed between two portions of a glass tube. In one 
of these a weighed quantity of mercury was placed and a 
thermometer. Into the other steam was blown, so that heat 
passed upward through the crystal and warmed the mercury. 
After taking a measurement in this position the apparatus 
was inverted, the mercury being placed in the other tube, and 
the steam directed into the tube formerly serving as the calo- 
rimeter. The glass tube chosen was about 20 millims. in in- 
ternal diameter, and about 1 millim. thick. It was divided 
into two parts, the edges fused and thickened and then ground 
flat, and very slightly smeared with a mixture of resin and 
Canada balsam. The crystal slice was placed between them, 
and they were bound together with strips of black caoutchouc. 
This joint was perfectly watertight. After a number of expe- 
riments in which the heat was made to pass through the crystal 
first in one direction, then in the other, the crystal was taken 
out, reversed in position between the two glass tubes, again 
secured in its place, and a fresh series of experiments were 
made. The condition of the crystal, as far as could be ascer- 

mal curres being obtained for low temperatures by tbe melting of films 
of cocoa-butter, and for bigJier temyeiatures by films of solid paiafliiis of 
definite fusing-point. 


Prof. Tliompson and Dr. Lodge on Unilateral 

tained, was the same after the series of experiments as before. 
The same "\vei<]jht of mercury (221 o;rms.) was employed 
throughout. The source of heat (the steam) was applied 
below the cry.stal in every case. The original temperature of 
the mercury having been read otf on the thermometer, the 
heat was a|)plied until the temperature rose through a given 
range — in the first experiment 50 degrees C, in the subsequent 
ones 40 degrees C. JMercury was employed as being more 
convenient in several ways, though a water calorimeter would 
probably be more accurate. The results of nineteen experi- 
ments, arranged in two series, are ap})ended in a tabular form. 
In this Table the faces of the crystal-slice are denominated a 
and /S. It was found by experiment that the face /3 corre- 
sponded to the analogous, a to the antilogous pole of the ori- 
sinal crvstal. 

Time occupied and 





direction of flow. 





1 U. 

a to /S. i /S to a. 1 1 

m s m s 1 In o 

I., II. 

50 3 30 


100:142 :i9 and 22 

/3 to « 

III.. lY. 

50 4 15 


100:141 22-25,, 23 

/3 „ cc 

v.. VI. 

50 3 40 

3 30 

100 : 04-5 15-5 „ 20 

/3 „ « 


Accident .... water boiled away. 


40 1 2 30 3 00 1 100: 120 !l7-5 „ 2125 


X., XL 

40 1 2 30 2 40 1 100 : 107 ilSTo „ ID'S 
Crystal then reversed between tubes. 

»,, /3 

I'., II'. 

Accidental escape of steam around calorimeter. 

III., lY. 

40 2 4.J 

3 15 100 : 118 ,25-5 „ 27 

/3 „ - 

Y., YI. 


3 00 

3 25 1 100 : 108-3 225 „ 2(V25 


Yll., YIII. 


2 35 

3 25 100 : 125 24-75 „ 2(i-25 

-.. /3 

Mean time-ratio 1 100 : 119 


It would appear therefore, by this method of experiment, 
that the ratio of the two conductivities in opposite directions 
through the crystal while it was beconn"ng hotter was roughly 
as 100 to liy. The more rapid flow is toward that pole 
which, when the crystal is Avarmed, becomes positively elec- 

Electrical Conductivity. 

It only remains to add, that the second-named of the authors 
has made -a few preliminary experiments Avith the view of de- 
tectino' anv unilateral conductivity of tourmaline for electricity. 
These experiments were made with the same slice of tourma- 
line, " B," as had been employed in the last-mentioned heat 
experiments — a crystal in which the faces were normal to the 

Conductivity in Tourmaline Crystals. 23 

crystallographic axis. The crystal was heated to 100° Centi- 
grade in a steam-bath. A 5-niicrofarad condenser was charged 
through the crystal with 10 or 12 Daniell's cells for a minute ; 
and then the condenser was discharged through a sensitive 
astatic Thomson galvanometer of 7000 ohms resistance. The 
conductivity of the tourmaline was so slight that the motion 
of the spot of light was only about two inches. The limit 
of swing was accurately observed, and then the operation 
repeated with the tourmaline (electrically) reversed. This 
was done again and again alternately in opposite directions. 

When the temperature of the tourmaline was rising, a 
distinct difterence was perceived between the to-and-fro dis- 
charge. Also when it was falling there was a difference, in 
the other direction. (These effects are of course due to that 
which is ordinarily termed electromotive force in the warming 
or cooling crystal.) But with a perfectly steady temperature,- 
which was only attained after some hours, not the slightest 
difference could be perceived. But before being satisfied 
with this imperfect and negative result, we should wish to 
use a battery of very much higher electromotive force (say 
1000 cells), and, if possible, heat the tourmaline above 100°, 
so as to increase its conductivity, which at 100° is sliaht. 

Note added, May 1879. 

Since the above was communicated to the British Associa- 
tion, a large number of attempts have been made to detect a 
different conductivity for electricity from a to j3 to that from 
^ to a when the temperature of the crystal was uniform. 
Numerous leakage methods have been employed, the most 
powerful having been one with a quadrant electrometer and a 
diy pile. Another slice, larger in area and only a millimetre 
thick, has been also used ; and the crystals have been tried 
when cold, when at 100°, and when heated up to 300° in an 
air-bath ; but although a small difference was many times ob- 
served, indicating a better conductivity in one direction than 
in the opposite, yet it always decreased, and i:sually vanished 
when excessive care was taken. It was very difficult to be 
quite sure that the temperature of the crystal Avhen hot was 
not slightly changing ; and the electromotive force due to such 
change of temperature was perceptible by the methods em- 
ployed when its direct effect on a quadrant electrometer was 
inappreciable ; and when the crystal is cold its conductivity 
is exceedingly small. It is intended, however, to try the best 
method once more, and more carefully ; and also it is intended 
to see if no difference can be perceived between the specific 

24. On Unilateral Conductivity in Tourmaline Crystals. 

inductive capacity of ;i cold crystal in opposite directions along 
its axis. 

So far, then, as experiment has at present gone, the results 
for the case of electricity have been altogether negative. For 
the case of heat, distinct results have been obtained ; but it 
is to be renienibered that a rising tenii)eraturo has always been 
used, and no experinients on the conductivity for Iwdt have 
been at present made with the tenij)erature constant : it is 
probable that, when they are, negative results will be also ob- 
tained corresponding with the negative results for electricity. 
AVehave roughly repeated the heat experiments with n falling 
temperature, and have obtained the ratio of conductivities in- 

Note hy the second-named Author. 

It thus appears that our original hypothesis with regard to 
the cause of the internal polarity of the particles of j)yroelec- 
tric crystals, at any rate in the form in which I ])ut it forward 
in section 26 of the paper " On a Mechanical Illustration of 
Thermoelectric Phenomena" (Phil. Mag. Dec. Suppl. 1876), 
has not been confirmed by experiment. 

But instead of this, the important result has been obtained 
by Professor Thompson that, in a pyroelectric crystal whose 
temperature is rising. Heat flows more easily icith the Elec- 
tricity (i. e. from the antilogous towards the analogous jiole) 
than it does against the electricity. This " convection of Heat 
by Electricity " has an apparent analogy with the effect j)re- 
dicted and verified by Sir William Thomson in unequally 
heated metals (Bakerian Lecture, 1856), and which might 
equally well be called the convection of Electricity hy Heat ; 
and it must have an interesting bearing on the theory of Prof. 
Kohlrausch concerning Thermo-electricity and Heat-condnction, 
set forth in Pogg. Ann. vol. clvi. p. 601. 

As to the original hypothesis, I am unable to give it quite 
up even now. For though I have no faith in unilateral con- 
ductivity in isotro})ic conductors like metals (uj)setting as such 
a thing Avould be to Ohm's law, which has been accurately 
verified), yet in hcmihedral crystals it did seem very jjossible 
that greater resistance should be ofi'ercd to the motion of elec- 
tricity in one direction through them than in the other, just 
as an ear of rye-grass is rougher one way than the other — that 
there should in fact be something analogous to barbs, or valves, 
so that when a. non-directional disturbance (like a uniform rise 
of temperature) was imparted to the crystal the electricity 
should be urged from a to /3 more strongly than in the reverse 
sense. Professor Maskelvne once told me that some crystals 

Frederick Guthrie on the Fracture of Colloids. 25 

were differently hard in opposite directions, so that they were 
more easily scratched in the sense AB than BA ; and if they 
possess one such unilateral property, they must surely have 
others. One surely ought to expect that a current driven 
through a pyroelectric crystal from analogous to antilogous 
pole would heat it, and that a current in the reverse direction 
would cool it, or heat it less. If, however, as I begin to fear, 
this is a wrong sceut, I should be very grateful to any one 
who will kmdiy point the fact out. — Oliver J. Lodge. 

III. Onjhe Fracture of Colloids. By FREDERICK GuTHRiE*. 

[Plates U. & ni.] 

§ 1. A PROMIXEXT property with regard to solid colloids 
Xa_ is that thev have neither crystalline form nor planes 
of cleavage. When such a body is broken it offers the so- 
called conchoidal fracture. An agglomeration of crystals 
mav present in mass the conchoidal fracture usually associated 
with colloids. This is the case with granite, and eminently 
so with basalt, all of whose constituents are crystalline. 
When the solid has resulted from the intersolution of two or 
more crystalloids it may, like glass, present the colloidal 
fracture in a most marked manner. And. indeed, even single 
crystals themselves are often subcolloidal in fracture ; that is, 
conchoidal fracture accompanies the crystalline. This state 
is shown by the diamond, sugar-candy, quartz, kc. 

I assume here that every cohesionally homogeneous mass 
of solid matter -^-ill break conchoidally when subjected to 
pressure sufficient to cause fracture. 


§ 2. Tlie cracking of a glass plate by pressure offers no 
special features of interest. A round plate placed on a thick 
soft cloth and pressed in the centre by a round cork cracks 
radially ; the cracks are generally slightly curved. Fig. 1 
shows two examples of fracture of crown glass by pressure in 
the centre. Similarly, if a round sheet of glass placed on a 
thick soft cloth be pressed down at its circumference by means 
of cardboard rings, the same class of crack is produced ; for, 
indeed, the two conditions are essentially identical. 

§ 3. The internal strain caused by difference of temperature 
causes fracture of great regularity and beauty. It rarely 
happens that a sheet of glass of any shape breaks into only 
two pieces when heated. If a circular piece of " crown " 

* Read before tlie Physical Society, March 22, 1879. 

26 Frederick Guthrie on the Fracture of Colloids. 

glass, about 3^ inches in diameter, be loosely balanced hori- 
zontally between the lips of a Avoodon clip and broucjlit with 
its centre over an air-gas burner so that the top of the flame 
is about an inch below the glass, the latter almost invariably 
cracks at least into three ])ieces ; and when the pieces are three 
in number they as invariably have the form shown in fig. 2. 

The remarkable symmetry of each of these, and their 
similarity to one another, show that the shape is not an 
accident of the glass. The constant features are (1) that the 
two main cracks join before reaching the circumference, 
(2) that there are in each crack, reckoned from this con- 
tinence, three concavities towards the centre of the circle, the 
first being nearly straight, (3) that there is a little kick 
given by the crack as it leaves. 

Out of sixty-four specimens of fracture produced under 
these conditions ten showed this species of two-crack fracture. 
The shapes of the cracks are perfectly similar to those given ; 
and the synnnetry is sometimes such that the side ]tieces may 
replace one another after inversion so perfectly that it is 
scarcely possible to tell that they are misplaced. 

§ 4. The same method of heating may result in the pro- 
duction of a great variety of forms ; but they are all derived 
from the above type. In fig. 3 are shown a few of the more 

The three-crack figures (o, o) are about as frequently 
formed as the two-crack figures. I find eioht of the three- 
crack out of sixty-four similarly treated specimens. Per- 
fectly similar forms were got when the plate was laid on a 
retort-ring or supported on three corks and heated in the 
same manner. A special series of experiments was moreover 
made to see if the ])osition of the clip had any influence upon 
the attitude of the crack. In figures 2 and 3 the mark f 
shows -SNhere the jilate Avas held. As to the effect of the posi- 
tion in the original sheet of glass of the pieces experimented on, 
as determining the attitude of the axis of cracking, the follow- 
ing examination was made. Six pieces having been marked 
as they lay in the sheet, Ibrming a radial band, were cut out 
and heated as above. The a})ex of crackagc always a})peared 
somewhere on the semicircle which was towards the centre 
of the sheet, but A-aried in this semicircle so considerably that 
it is at present doubtful Avhether the position in the sheet in- 
fluences the. crack-axis. Fig. 4 shows the amount of varia- 
tion ; the point of the arrow re})resents the ajx'x of the crack- 
curve. The loAver figure represents the original sheet and 
the positions of the several pieces in it. 






PM. Mao. S. 5. Vol. 8. Pl.IIL. 

Fig. -■' 


Fi^. 8. 

Fig. 9. 

Frederick Guthrie on the Fracture of Colloids. 27 

§ 5. If the sheet of glass be made very much larger, or the 
flame smaller and more pointed, another alteration of the 
crack-figure ensues. The apical point of the previous figures 
advances into the sheet ; and this is followed by a fan-like 
cracking of the glass between the apex and the still nearest 
circumference. In fig. 4, a shows the cracking of a plate 
of crown glass, 9 inches in diameter, over an air-gas burner ; 
b is a 5|-inch-diameter plate similarly treated. In c we have 
a plate of crown glass, o inches in diameter, which was laid 
on a cloth and heated from above by a fine blowpipe-flame. 
If we conceive what was before called the apical point to reach 
the centre, the heat fracture would become approximately the 
central-pressure fracture, namely radial. 

§ 6. A piece of plate-glass ^ inch thick and a little over 
7 inches in diameter, cracked when heated in the centre over 
an air-gas burner, as shown in fig. 5 a. A piece of " sheet- 
glass " (Chance's), 3 inches in diameter, cracked as shown in 
h. A slab of resin | inch in thickness and 3^ inches in dia- 
meter, heated in the centre by a jet of low-pressure steam, gave 
the fissures shown in c. Square porcelain tiles cracked nearly 
straight across in one crack. 

§ 7. Pieces of crown glass of various shape were next 
examined, with the result which declares itself in fig. 6. The 
pieces were supported at the point marked c, and the flame 
applied below the point marked f. 

Tlie figure 6 shows that the same general type is preserved. 
It instructs us that the apical point seeks one of the nearest 
points of the circumference. 

§ 8. Experiments were next made for the purpose of as- 
certaining under what circumstances, if at all, a crack could 
cross a crack. A circular plate of crown glass was cut by the 
diamond in concentric rings, and the crack was made to pass, 
by ta])ping, completely through the thickness of the glass, 
around the whole circumference. Such di^^ded glass on beino- 
heated in the centre over an air-gas burner cracked according 
to the same type as before. Sometimes the heat-crack would 
run across the diamond-crack, as though the latter had no 
existence. Sometimes the heat-crack would follow, and, as 
it were, adopt the diamond-crack, and then break off. In the 
latter of such cases the inner circle may be suffering a three- 
crack fracture, Avhile the outer ring exhibits only a two-crack 
fracture on the converse. Fig. 7 (a) exhibits the former 
circumstance, fig. 7 (b) shows the influence of a greater 
number of concentric cracks. 

§ 9. The heating of the central part of a circular plate 

28 Frederick Guthrie on the Fracture of Colloids. 

should pive the same crack-fi(;ure as the eoolinfr of the cir- 
cumference ; and, as a matter of exf)erimeut, it is found that 
the figures are very similar. In order to cool the circum- 
ference of a heated circular plate with some aj^proach to 
uniformity, an annular trough was constructed by cementing 
concentrically two glass cylindrical vessels of the same depth 
but diti'erent diameters, one inside the other, and over-filling 
with mercury, so that the convex surface of the metal pro- 
jected. The glass was held in a wooden clip widely stretched, 
so that the axis of the clip being vertical the plate was hori- 
zontal. Held, when uniformly hot, immediately above the 
mercury, it was let drop and pressed down in the middle by a 
piece of wood. The fracture is in this case instructive ; for 
while in fig. 8 (a) the old type got by heating the centre is 
resumed in h and r, the fracture is either influenced or even 
accompanied by the circular fracture along or near the line of 
greatest temperature-difJ'erence. 

§ 10. It is clear that heating in the central regions should 
produce a smiilar fracture to that brought about by cooling 
around the circumference, and cooling at the centre a similar 
fracture to that caused by heating the circumference. 

On heating a circular plate at the circumference by means 
of a " rose "" air-gas burner, it breaks with far greater violence 
than when fracture is produced by central heating. The 
parts are scattered at least three times as far in the foniier as 
in the latter case. The form of the fracture is essentially 
radial ; but the fragments, even Avhen the primitive type is 
widely de})a)-ted Irom, })resent wonderful symmetry. A 
noticeable point in this fashion of fracture is the invariable 
appearance of two ])ieces on opposite sides of the centre whose 
form is approximately rectangular ; that is, their sides are half- 
cords instead of radii. This form suggests that there are two 
chief centres of maximum fracture, and that the bounding 
radii of the two systems are parallel. In fig. 9 the pieces 
marked a re])resent these singular })ieces. Out of seven plates 
which have been broken in this way, there is not one in which 
this feature is absent. 

§ 11. As to cooling a hot plate in the centre, I find snch 
extreme difficulty in reproducing the inverse conditions of 
heating a hot plate at the circumference that I have rarely 
succeeded in re})roducing the same type of fracture. 

Also it is seldom the case that a sheet of glass cracks during 
heating at its edge. More frequently a sheet of glass which 
lias been heated at its edge cracks when cooling. The crack 
then appears to follow that isothermal line along which there 

Frederick Guthrie oa the Fracture of Colloids. 29 

is the greatest difference of temperature at right angk^s to 
the line. 


§ 12. About the fracture by mechanical strain it may 
appear to satisfy many that the lines of fracture are perpen- 
dicular to that resultant of the pressure which lies in the 
plane fractured. A tear in a sheet of paper is at right angles 
to the two opposing pressures, or rather to their resultants at 
the point yielding. 

What is a crack ? Which are its beginning and end ? In 
only one of the aboye-cited experiments can the growth of a 
crack be followed. In § 11 when a plate heated at the edge 
has refused to crack while being heated but cracks on cooling, 
the crack is seen to extend from the edge of the plate inwards, 
following, generally speaking, a semicircular path, but some- 
times curiously modified towards the centre of the curye. 

A crack is neither a line of least cohesion nor a line of 

greatest strain. ISTor is it a line where - has a series of niini- 
*= s 

mum values. The more perfectly elastic a medium is, the 

more fully does the crack resemble a flash of lightning or 

wisely laid railway-line, and the more it departs from the 

river-course or the descent of a globule of mercury down an 

inclined but undulating surface. Its path is the curve whose 

course is determined by the integnal of - being a minimum. 

The sudden splitting through of the solid sether by the electric 
discharge furnishes us with figures by no means remotely re- 
sembling those of the fracture of glass. Even or rather 
especially the forms of fig. 4 remind us of this. 

As to the ty{)ical form in fig. 2, it has been suggested by my 
brother, Mr. Charles Guthrie, that this form is a compromise 
between the circular line of fracture along some isothermal 
line where the difference of temperature is greatest, or rather 
the difference of expansion is greatest, with the three lines of 
relief which would be radii at angles of 120° with one 

This is a very suggestive hint ; but, for reasons sufficiently 
apparent from the foregoing, it is insufficient. 

[ 30 ] 

IV. On a neglected Principle that mat/ he onploi/cd in Earth- 
quake Measurements. Btj John Perry and W. E. Ayrton, 
Professors in the Imperial College of Engineering, Japan*. 

[Plate IV.J 

SPECULATIONS regarding the internal constitution of 
the earth have interested philosophers for many years. 
For a long time it was considered that our globe consisted of 
a thin solid shell containing a fluid core : but Hopkins, who 
was one of the first to investigate the subject on correct prin- 
ciples, showed that this shell must be from 800 to 1000 miles 
in thickness; and still more recently Sir Wm. Thomson has 
proved that the apparent absence of elastic tides in the earth's 
surface leads to the conclusion that the average rigidity of the 
earth is greater than that of glass, and possibly even greater 
than that of steel. AVe do not on the present occasion propose 
to consider whether the state in which the internal part of the 
earth exists is like any state of matter with which we are ac- 
quainted ; but this is, of course, a subject well worthy of very 
careful investigation. 

It is probable that the earth was once in a molten condition 
and that it now is cooling ; so that the shrinking resulting 
from this cooling must develop vast internal forces, producing 
strains, or deformations, of great magnitude. Other powerful 
forces, too, brought into existence by water being suddenly 
changed into steam on entering a hot cavity, by the sudden 
chemical combination of gases, or possibly by elastic tides in 
the earth's substance produced by the joint attractions of the 
sun and moon — all tend to cause disturbances and ruptures 
which are brought vividly to our notice by voleanos and 

An earthquake has been defined by Mr. Mallet as "the 
transit of a wave, or waves, of elastic compression in any di- 
rection, from vertically upwards to horizontally, in any azi- 
muth, through the crust and surface of the earth, from any 
centre of imjnilse or from more than one, and which may be 
attended with sound and tidal waves dejiendent upon the im- 
pulse and upon circumstances of position as to sea and land." 
If we could only read the earthquake message rightly, we 
should learn all about the deformation going on in the earth's 
crust ; for there is no doubt that the nature of the stresses 
and strains, and every condition of the rocks at the origin of 
motion, all give their character to the earthquake vibrations. 
It must be remembered, however, that the message before it 

* Communicated by the Authors, having been read before the Asiatic 
Society of Japan on the 23rd of May, 1877. 

PMMa^. S. 5. Vol. 8. PI ]\^. 

On Earthquake Measurements. 31 

reaches us is mucli modified by the media through which it 
has been transmitted ; and, again, since there is a great want 
of continuity at the surface of the earth, very important mo- 
difications are introduced by surface conditions : for example, 
rano-es of mountains are well known to reflect earthquake 
vibrations in a marked manner; and veins of good conducting 
rock, by transmitting the vibrations more rapidly than less 
conducting veins, set up transverse vibrations. 

Professor Palmieri and others have invented instruments 
which record the date of the vibration, and give rough ideas 
of the direction of propagation of the earthquake-waves, 
together with what is called the strength of the vibration. 

Mr. ]\Iallet, whose wide experience on the subject of earth- 
quakes has necessarily caused his writing to be regarded with 
great respect, describes the object of Professor Palmieri's in- 
strument as follows : — " By means of this apparatus the time 
of the first shock is recorded, as well as the intervrl between 
the shocks, and the duration of each : their direction, whether 
vertical or horizontal, is given, as also the maximum of inten- 
sity." He further says, however : — " It is not my intention 
here to offer any criticism as to the construction or perform- 
ance of this instrument, the rather as I must confess I do not 
quite share the high opinion of its inventor as to the certainty 
or exactitude of its indications." And this opinion of Mr. 
Mallet with regard to Professor Palmieri's instruments is ours 
with regard to all the seismoscopes of which we have read any 
descriptions. Indeed it is well known that the instruments 
hitherto invented have not satisfied even the modest hopes of 
their inventors; whereas, even if these hopes had been fulfilled, 
we should still hardly have made a step in this new science. 

A simple form of seismoscope, but by no means a perfect 
one, would be a lamp suspended from a ceiling by a spiral 
spring, of such a strength that the period of vibration of the 
lamp in a vertical direction was nearly the same as that for its 
vibrations when swinging as a pendulum. The A'ibrations of 
such a lamp during an earthquake would contain motions due 
to the motion of its point of suspension ; and an experienced 
observer would be able during a shock, or very soon after it, 
to tell the direction and strength of the shock with much more 
accuracy than with any of the instruments previously described. 
This lamp seismoscope, however, possesses the defects of all 
slowly vibrating bodies : the main vibration of the lamp is (as 
we shall presently show) executed in its ordinary periodic 
time ; and the lengths of its swings depend on many other 
things besides the strength of the shocks, which would show 
themselves as small perturbations in the motion of the lamp. 

32 Professors Ferry atid Ayrton on a neglected Principle 

If, however, instead of actually observing tlio lamp we merely 
get a record of its greatest swing, then very little information 
could be obbiined of the strength of the shocks ; for the great 
or small deHec;tion of a slowly vibrating pendulum during an 
earthquake will dejjcnd on whether the period of the earth- 
quake is or is not some submultiple of the period of the pen- 
dulum; so that considerable mathematical knowledge and much 
time would be requisite to deduce from the comparatively 
small ripples on the larger vibrations the nature of the earth- 
quake, hi addition, as the length of the swings of the lamp 
will generally bo much greater than the earthquake vibrations, 
they will, if recorded on paper, require a very large recording 

We now proceed to the principle which is to enable us to 
record an earthquake-message. It must be evident that the 
message can only be correctly recorded when we have obtained 
the complete motion at every instant of time during the earth- 
quake of a large portion of the rocky crust of the earth. Any 
point P in the solid earth has a certain position, a certain ve- 
locity, and a certain acceleration in a certain direction in any 
instant of time during an earthquake ; and if we know these 
elements we are said to know the motion of P. Now we have 
a complete record of an earthquake when we know the motions 
of all points P affected by the earthquake ; and if the earth 
were rigid, this could be derived from a knowledge of the 
motion of three of its points not in the same straight line. 
Still, although the earth is not rigid, and although the condi- 
tions of motion, of ditferent parts of an elastic non-homoge- 
neous solid are very complicated, we may say that the important 
character of an earthquake, its origin and the media through 
which it has travelled, as well as its rate of motion, are recorded, 
and may perhaps be easily deduced from the known motions 
of three well affected points in the solid earth. Believing this 
to be the ease, and seeing how important it is to the whole 
science of terrestrial physics that the earthquake-message 
should be read, we have been led to investigate mathematically 
the motion, during an earthquake, of a body attached to the 
earth by springs. And we have come to the conclusion that 
the centre of mass of a body fastened by means of springs 
inside a metal box rigidly attached to the earth, has in certain 
cases motions with respect to the box itself which in miniature, 
with great exactitude, represent the motions of a point of the 
box during the earthquake — this result being truly obtained 
when the springs are exceedingly strong, so that the motion 
of the mass relatively to the box is exceedingly small, and 
practically obtained when the springs are so strong that the 

that may he employed in Earthquake Measurements. 83 

vibrations possible for the mass when there is no earthquake 
are several times quicker than the earthquake vibrations them- 
selves ; that when the springs, however, are weak, the motion 
of the mass relatively to the box in no way represents the ab- 
solute motion of the box itself ; but that the introduction of 
friction, although it diminishes the accuracy of observation of 
regular vibratory earthquakes made by means of very rapidly 
vibrating springs, makes it possible to get an approximation 
to accuracy even with slowly vibrating springs, and is always 
desirable when the earthquake vibration is irregular and in- 
termittent. In fact, in order that the motion relatively to the 
box of the centre of mass of the body supported in it may 
accurately represent the real motion of a point of the box itself, 
it is necessary that the mass be large, and the springs sup- 
porting it so strong that its natural time of vibration shall 
be about five times as fast as that of the earthquake itself, 
supposing no friction be employed beyond that necessarily in- 
troduced by the mechanism of the recording apparatus : or a 
much larger mass may be suspended by weaker springs if the 
chamber be filled with water, or some oily or tarry compound 
which will introduce the necessary amount of friction. 

Let A B (PL lY. fig. 1) be a rigid box firmly attached to the 
earth; M is a large mass acted on by two horizontal springs, 
and subjected to no forces except those introduced by the 
springs, its weight, for example, being neglected. When both 
the box and M are at rest, let their centres coincide at the 
point C. 

First let the box be at rest, and let M be made to vibrate in 
a horizontal line passing through its centre, and let y he its 
distance at any time t from a point fixed in space ; then 

^ = -n%-OC), (1) 


(3/-OC) = Pcos(«f + Q); 

where P is the amplitude, and where 


T being the periodic time. 

Next let the box be in motion in a horizontal direction, and 
let z be the distance of its centre from the fixed point at the 
time t ; then 

cP{y-z) _cPy cPz_ <Pz 

dt^ ~dt' de~ ^y ^^ dt^' 

Phil Maq. S. 5. Vol. 8. No. 46. Jul,, 1870. D 

o4 Professors Perry ami Ayrtoii on a neglected Principle 
from (1). If tlio velocity of tbe box iis uniform, 

therefore tlie relative motion of M about tbe centre of tbe box 
is a simple barmonic motion. 

Let tbe box bave a uniform liorizontal acceleration a, tben 

cie V '^ nO' 

therefore tbe body M bas a simple barmonic motion about a 
point at a distance -^ behind tbe centre of tbe box. 

Now, whatever be tbe forces acting on the box or tbe ball, 

de df de ' 

or the acceleration of tbe ball relative to tbe box equals the 
absolute acceleration of tbe ball minus that of tbe box. 

Let M be resisted with a frictional force proportional to its 
mass and to its velocity relative to the box, let 2/ be tbe fric- 
tional coefficient, and let the earthquake vibration be a regular 
barmonic motion about the fixed point ; tben 

^!(|Z£) = -2/^i^ - n-Xy -c) + n^, A cos {n,t + B), 

where A is the amplitude of the earthquake -sibration, and 


Ti being the periodic time of the earibquake vibration. If 
when tbe time is nought tbe box is at tbe limit of its swing, 
then B is nought, or 

"V = -^'T -"'f^--) + "' ^ '"' '"' ■' 

from whicb, substituting x for^— ~, we get 

d-.v „ ,. dx - „ . 

^TT = — 2/ -7- — 71', r + ??*A cos nit 

dt- at ' 

as the equation of relative motion of the centre of M. Now 

. . AttK 

the maxnnum acceleration oi tbe box is 7?,A, or ■ „,^ ; con- 

sequently, if this acceleration were constant, and if there were 
no friction im])eding the motion of M, the mean position of 
tbe centre of M would be behind tbe centre of tbe box bv a 

that may he employed in Earthquake Measurements. 35 


or T^ 

Let this distance be numerically equal to E, then 

-7-r +2t^- +nM" — ?rEcos«i^ = 0. 
dt- ^' dt 

Section A. 
The first and at present the most important case to consider 
is when /is less than 71*. 

The integral of this equation is 

E?r cost ?ii^+ tan" 2_ 2 ) 
.v=.-'/Dcos(v/g^. + F)- ^(„._„y^,„:). " ' ■ (2) 

For facility of calculation we assumed above that the box was 
at the limit of its swing when the time Avas nought. We must 
now make some assumption with regard to the initial position 
of M in the box. As the most important point to consider is 
Avhether M, by its motion relative to the box, correctly records 
the vibration of the box when this vibration in some way sud- 
denly alters its character, we arbitrarily assume that, when 
the time is nought, M is at the limit of its swing in the ])Osi- 
tive direction — since we know that if the vibration of the box 
did not alter its character, and if M were pre^-iouslv correctly 
recording, then at time nought M would be at the limit of its 
swing in the jiegative direction. 

When ^^Q^ 

1^* .r = E, 

^ii'^ d,v 

By substituting in (2) these values, we find 

cosF^^{l+^ (-^--^) I 
D I {n^^-n''y + 4.n\fy 

^{n'-Dlinl-n-'f + ^n\f^ ' 

* This is the condition wliich allows M, when disturbed, to swing about 
its position of equilibrium with an infinite number of decreasino: deflec- 
tions right and left. As/ increases, we see, on examining the first part 
of the integi-al, that the periodic time of M about its position of rest be- 
comes longer and longer, and the swings of M diminish more rapidly in 


3(J Professors l\'i-ry aim! Ayrtoii on a neglected Principle 

so that, given n,ni, 2/. and A, we can find the position of M 
with respect to the centre of the box at every instant. 

I. Let there be no friction impeding the motion of M in 
the box — that is, let/ equal nought, then equation (2) becomes 

.r= i— cosn< 5 .fCoanyt, 

n^-n^ ii\-n^ ^ ' 

a composition of two harmonic motions of different periods 
and am})litudcs ; or it may be expressed as 

.r = distance of centre of M from the centre of the box due 
to natural vibrations of the spring without earthquake. 

— distance of the centre of M from the centre of the box 
due to earthquake motion, M being supposed to have 
no natural vibrations due to the springs. 

Now if we want the relative motion of M to represent the 
earthquake vibration, we must have 

En- En'* 
many times greater than L_, 



«f — n' 

Ti many times greater than T. 
For example, let the springs be so strong that 

that is, 

nz=\Qni ; 


.V= — ^^ cos 7lt + COS Hit ; 

or the vibrations of M due to the natural vibrations of the 
springs have an amplitude only j^^jth part of the vibrations 
of M which r(!ipresent the earthquake. In fact M by its rela- 
tive motion in the box merely records the earthcpiake vibra- 
tions, to a scale diminished nearly in the ratio of n^ to n^^, or 
as 100 to 1, and the natural vibrations of the spring are quite 

If now we take the opposite case where the springs are 
weak, so that the natural vibrations of M are slower than the 
earthquake vibrations, we find, supposing 


9E E 

.r= — - cos nt— cos ^i^ ; 

o o 

that may he emphn/ed in Earthquake Measurements. 37 

that is, the amplitude of the motion ]\I relative to the box 
caused bv the natural vibrations of the springs is nine times 
as great as that due to the earthquake vibi-ations. 
II. Let 

and let the springs be strong so that M has a natural vibration 
quicker than the earthquake vibration. For instance, let 

T, = 10T, 

w = 10??i; 

then, from (2), the general solution for/' less than n, we find 
A.=e-5''.^ Jp- cos (8-66/21^ + 90°; -E cos (m 1^-5° 46'). 

Now when t is nought, the first term, which is due to the 
natural vibrations of M independent of the earthquake, is 
small compared with the second term, which is due to the 
earthquake itself; and, in addition, as t increases, the first 
term grows rapidly smaller ; therefore we may say from the 
beginning x represents the position of M due to the earth- 
quake only, and is independent of the natural vibrations of M. 
Now let the springs be weak, so that they have a natural vi- 
bration slower than the earthquake vibration. Let 


«'' «i = 10«, 

''''"^ f=kn, 

as before ; then 

a-=e~ is X 1-16E cos (l-16«if + 80° 5')- -^. cos {n^t + 5° 46). 

At the beginninor we see that the natural vibrations of M 
greatly preponderate, and that it is not until 

^=5 log 111-4 

that the amplitude due to the natural vibrations becomes di- 

minished to -—,. After this time the vibrations due to the 

earthquake begin to preponderate and eventuallv entirelv 

mask the others, and the amplitude becomes —, — that is, a little 

greater than A or the amplitude of the earthquake vibration. 
It is interesting therefore to notice that, with a Aveak spring, 
using friction, although the vibrations of M do not re])res('nt 

38 Professors Perry and Ayrton on a neglected Principle 

the earthquake vibrations at the beginning, they do after some 
tinio if tlio cartliquako only lasts long enough, and continues 
to bo exactly the same pure harmonic motion. 

Section B. 
Let the friction bo such that 

then the solution of the differential equation becomes 



we find 


\ n^^—n-j 



t = 0, 

G_n\ + Sny 
E" (n] + n-y' 

H_ n^^7l 

n^ + n-' 

Let the springs be strong, and 

7i = 10ni, 

If tho springs are weak, and 

n^ = 107i, 


^/10300 ,100 \ E / , , , ,20\ 
^ (i0201 + 10l"^7- 101 '''V'' + ^'" 99> 

These results are of the same nature as before : with the 
strong springs we see, since e~^°"'* is small compared with 
■|-J]^-, that .V represents the displacement due to the earthquake 
only; Avith the weak springs, when t is small, the natural vi- 
brations of M preponderate and mask tho earthquake-effect ; 
but as t increases, these vibrations become smaller relatively 
to those due to the earthquake, so that the weak springs will 
eventually record the earthquake if it only lasts long enough. 

that may he employed in Earthijuake Measurements, 30 

Section C, 

then the general solution of the differential equation becomes 

. \ 11^ — n-) 

.r = c-/' D cos {iWf- - n-t + F) . ,^^ =^^ • 

as before, the vakies of D, E, and j:) must be determined from 
the character of the motion when t is nought. 

When /is equal to or greater than ??, then an examination 
of the first term of the solution shows that M has not a natural 
vibratory motion ; but if deflected from its position of rest 
when there is no earthquake, it will gradually approach this 
position but never reach it. 

Although, therefore, the first term of the above solution 
rapidly disappears (that is, the natural vibrations of the springs 
die away, whatever be the strength of the latter), still the ap- 
plication of recording apparatus, and the necessity that M 
shall reach its mean position in a reasonably short time after 
disturbance, have caused us to restrict ourselves to cases in 
which /is less than n*. 

At the commencement of section A, it was explained that 
the box and mass M were both assumed to be deflected from 
their positions of rest when the time equalled nought. It must 
now be observed that M Avas supposed deflected to the opposite 
side of the centre of the box to that towards which it would be 
deflected on the box receiving; a shock : and the followino- in- 
vestigation will show that that assumption really corresponded 
with a sudden change in the form of harmonic motion in ac- 
cordance with which the box was moving, or what may be 
called a discontinuity in the motion of the box. For while 
we have proved that, with our original suppositions, the motion 
of the box was instantaneously recorded by the motion of M 
if the springs were strong, but that if they were weak the 
early vibrations were lost, and that it was only after some time, 
and then only provided the earthquake lasted long enough, 
that a record was left, we shall now prove that, if the earth- 
quake be regular tcithout any discontinuity ichatever (which, 

* The results arrived at in the previous sections may be easily slioAvn 
experimentally by using -sveak and strong springs, so as to give M a natu- 
rally long or short period when it is set in vibration by shaking the frame 
to -which it is attached. The motion can be magnified and indicated bv a 
long light pointer moving over a scale rigidly attached to the frame, and 
the etfects of inta-oducing various amounts of friction shown by causing 
the pointer to rub with more or less force against the scale. 

40 Professors Perry and Ayrton on a imjlected Principle 

however, our experience of earthquakes in Japan leads us to 
believe is rarely the case), then weak sprino;s will give good 

Section D. 

Let the earthquake motion be a })eriodic function of the 
time ; then we know it may be expressed in the form 

c = Ao + 2Acos(N< + F), 
where A, N, and F may have any values we please in the 
successive terms of the series. Or, generally, it may be ex- 
pressed in the form 

c = 2Acos(N< + F), 

one N haA-ing a value nought. 
Let us take the restricted case 

c = 2AcosN<; 
then, if there is no discontinuity at the beginning, 

2 = 0, 



/ = 0; 

from which it may easily be shown that 

2 = 0. 

The differential equation of the motion of the centre of the 
mass M relative to the box is 

f? + 2/'^ + n2.r=n22EcosN^ 
at- ' at 



for each value of A and X taken in the successive terms of 
the series. The solution of this differential equation is, if/ is 
less than w, 

.r = ^-/' C cos (v'/r— /-V + D) 

— n-z, , , . (o) 

the constants C and D being determined from the initial con- 
ditions, which are, when 

/ = (>. 

that may he employed in Earthquake Measurements. 41 


dx _ p. 


from which it follows that 

CcosD = n-2J, 




^ 2EN- 

It is obvious that we want the coefficients in the above equa- 
tion for X to be proportional to nought, Aj, Ag, A3, &c., and 

2N t 2\. f 

also the epochs tan"' W~2j tan"^ ^^^ 3 , &c. to be all nought 

if we are to have a perfect representation of the earthquake. 
Now for the epochs to be very small, / being a reasonable co- 

efficient of friction (sav/ equals ^w), we must have ^-^ either 

verv small or Acrv laro-e. Examining; the coefficients of the 
second part in equation (3), 


v/(xNl-nO^ + 4Xy^'' •' 



we see that the condition ^ being very small will make them 

proportional to Aj, A2, &c., as is required for a perfect repre- 
sentation of the earthquake motion ; and if we put the coeffi- 
cient C into the form 



(1-0 + 4^ 
+ -^ 2-A- 


42 Professors Peny and Ayrtou on a neglected Principle 
we observe that Avhen ^ is vert/ small and / the same as above, 

Now, as 2 A boino; equal to nouglit, as previously shown, is the 
condition of contiuuity, C disappears ; and hence all earth- 
quakes Avhich haAO continuity from the beginning, and which 
are expressible in the form 

z = 2 A cos N^, 

are perfectly represented if n is very small compared with 
every N — that is, if the natui*al vibration of the spring has a 
period much longer than the period of any element of the 
earthquake. This also introduces the additional restriction 
that no N can be very small ; consequently z cannot have a 
constant term. If in the above /is nearly equal to ?/, then 

C = a very large number x 2A. 
If 2A is absolutely nought, then the size of the multiplier is 
of no consequence ; but if 2A is not absolutely nought (that 
is, if there is a slight discontinuity), then C may be very 
large ; so that with more friction the failure of the weak 
springs to produce an accurate registering appai'atus is very 
much more marked. And since the coeflicient e~-^' is greater 
than <?""' and e~""' is large since n is small, it follows that e~-^' 
will be large, and will not rapidly reduce the value of the first 
term (which may be said to belong to the natural vibrations of 
the springs) in equation (3) for x. 

We shall now consider the alternate condition, viz. 

5 very large; 

I. e. 

very small, or the springs very strong. 

The coefficients in the second part of equation (3) may be 
put in the form 











that may he employed in Earthquake Measurements. 43 

and as ^ is assumed to be equal to x, "^e see that the denomi- 

nator may be regarded as constant and very little less than 
unity ; consequently the second, third, &c. terms of equation 
(3) wiU be proportional to A^S'l, AoX^, &c. It follows there- 
fore that the elementaiy ^-ibrations of the earthquake, of smaller 
periodic times than the rest, will, in the representation, have 
greater amplitudes than they ought to have. If, however, 
the elementary periods are not very unequal, the curve drawn 
by the seismograph will be a fairly approximate representation 
of the earthquake. 

C may be expressed in the form 




\n- } 11- 

or, since"—, equals -, and ~ is very small, 
' /r ^ 4 n " ' 

f ^ AW 


therefore C is a very little less than the algebraical sum of the 

other coefficients; and if we suppose, as above, that the values 

of Xi, Xo, &c. are not very ditferent, then, since SA equals 

nought, it foUows that S — ^, and therefore C, cannot be very 


A^e therefore conclude that, in the case of an earthquake 
represented by the equation 

both weak and strong springs give good results. 

As an example, let the earthquake motion be represented 


^ = A (cos id— cos ^1 id), 

the curve corresponding with which is shown by the thick 
white line 7 7 7 in fig. 2, the thin line a a a being 

.r = Acos^-^, 
and the thin line /8;S/3 

.t-= -A cos ^^Id. 

44 Professors Perry and Ayrton on a neglected Fi-inciple 
Let the springs be strong, so that 

and let 

then, determining the values of the constants, we find 
.f = -c-5-5'* X 0-00458 A cos (9-62 ht + 0-5142) 
-0-00814 A cos (^^ -0-0917) 
+ 0-01218 A cos Ogi A'^-0-1096), 
the curve corresponding with which is shown by the thick 
white h'ne Hi in fig. 3, the thin line 88S being 

.,,-= - €~^-M X 0-00458 A cos (9-62 kt + 0-5142), 
the thin line rjrjr] 

.r= -0-00814 A cos (/(r^-0-0917), 
and the thin line 6 69 


This curve (i i i) is magnified so that the greatest amplitude 
is nearly the same as the greatest amplitude in the real earth- 
quake motion. 

If the springs remain as before, but if there be no friction, 
then, determining the constants, we find 

.1'= -0-00408A cos (11-i kt) 

-0-00816 A cos (^-f) 

If the earthquake be represented by the same equation as 
before, and if 

n = U 

then equation (3) becomes 

a;=-g-i*'x 0-071831 A cos (2-55 yl-< + 0-78015) 

-0-11704 A cos (A'^-0-35896) 

+ 0-17877 A cos (^/(•<-0-45408); 

the curve corresponding with which is shown by the thick 
wliite line vvv (fig. 4), the thin line kkk being 

.,. = _ e- If^t ^ 0-071831 A cos (2-55 kt + 0-78015), 
the thin Hue XXX 

.(■= -o-ino-l A eos (^•/-0-o5896), 

that may be employed in Earthquake Measurement f^. 

and the thin line /"-/ti/A 



4() Professors Perry and Ayrton on a neglected Principle 

Section E. 

Let us now consider the case when 


then, unless n equals N, all the epochs are nought; so that, as 
far as the epochs are concerned, no restriction is introduced 
in making the seismograph-curve exactly represent the earth- 
quake. C may be put into the form 

so that if n is small compared with every N (that is, if the 
springs are weak), then 

C = 2A nearly, 

= nearly, 

since SA = is the condition of continuity; and the coefK- 
cients of the second part of the right-hand side of equation 
(3) are 

which are equal to Ai, A2, &c. Therefore weak springs give a 
very good representation of the earthquake. 

It must, however, be remembered that, although in the case 
of an earthquake motion having no discontinuity, w-eak springs 
give good results, sometimes even better than strong springs, 
still in the most complicated cases, if .the natural vibrations of 
the springs be quick, a little experience will enable easy cor- 
rections to be made, which will allow the real earthquake mo- 
tion to be read with much greater accuracy from the represen- 
tations than might at first sight appear from the formulae. 

Section F. 
Without the help of actual experiments made with the form 
of seismograph we propose, calculation leads us to infer that 
with a small amount of friction, such as that opposed to a lead 
ball, of sav 400 lbs. mass, surrounded by water or oil, and 
with the ball moving a simple recording apparatus, strong 
springs will always give nmch more satisfactory results than 
weak ones for earthquakes such as we have felt in Japan ; but 
since friction will always cause the natural vibrations of the 
ball to cease in a longer or shorter time according as the fric- 
tion is small or great, it is possible that very satisfactory 

tliat may he employed in Earthquake Measurements. 47 

results may be obtained by using weak springs and surround- 
ing the ball -svith some more viscous liquid, such as treacle or a 
mixture of tar and pitch, if only the alteration of viscosity by 
change of temperature can be readily compensated for, and if 
it be possible to easily employ a good recording apparatus 
when using much friction. On the whole our calculations 
point to the employment of a small amount of friction and 
strong springs ; but for the following reasons we feel that our 
calculations should be chiefly employed only for directing and 
making use of experimental knowledge : — first, because we 
assumed the friction to be proportional to the mass of M and 
to its velocity, whereas in reality the friction is probably com- 
posed partly of a constant term depending on the recording- 
apparatus, and partly of a term proportional to the square of 
the velocity of M, and to a certain extent proportional to its 
surface ; secondly, because extremely little is at present 
known regarding the nature of the earthquake shock. Even 
the period of an earthquake vibration does not seem to have 
been measured with any approach to accuracy ; the informa- 
tion obtained in some cases from the stopping of clock-pendu- 
lums is quite unsatisfactory, since the limits between which 
we can place the period of earthquake vibrations so as to stop 
an ordinary pendulum-clock are wide apart. 

Section G. 

Fig. 5 (PL IV.) shows roughly our first idea of the construc- 
tion of a seismometer in accordance with the principles we have 
enunciated. A leaden ball of some 400 lbs. mass is supported by 
five strong spiral springs inside a strong iron case, rigidly fixed 
to the rocky crust of the earth ; four of the springs are horizon- 
tal, and one vertical, and all have the same period; so that if 
there were no friction the centre of mass of M would describe 
an ellipse when M is freely vibrating. In order to get a record 
of north-south, east- west, and up-down motion of M, three arms, 
two of which (A B, C D) are shown in the figure, carry pen- 
cils pressed by means of small spiral springs on a band of 
paper moved regularly by clockwork in a horizontal direction 
at right angles to B D — the clockwork, as in Professor Pal- 
mieri's and other instruments, being set in motion at the com- 
mencement of the earthquake. The arm AB is rigidly fixed to a 
small piece AE at right angles to it (see figure of ball enlarged); 
this again by means of a pivot at E is fixed to E F, Avhich is 
rigidly attached to the ball. A pin at A, supported by the frame- 
work of the instrument, allows A B to move round it, and so to 
record vertical motions of the ball ; and the pin A, having a 
certain amount of lateral motion in the slot; combined with the 

48 Professors Perry mtil Ayrtuii nn a ncijJcrtt'd Principle 

shape ol' A E F, prevents A P recordinir any lateral motions, 
since the motion of A P parallel to itself is so small as to be im- 
perceptible. C J) turns about the pin C, and is prolonged to G, 
where it is attached by a pivot to an eye rigidly attached to 
the ball : G C D therefore records lateral motions in one direc- 
tion, say north-south ; but is not ett'ected by east-west motions 
or by vertical motions of the ball, as these latter only cause 
tlie pin C to move vertically in the slot. The third arm, not 
shown in the figure, by a somewhat similar ai-rangement of 
levers, only records east-west motions. All the motions are 
recorded on one plane, on tlie same band of paper; so that the 
curves would be somewhat as shown in fig. G. Drawing any 
line A P at right angles to the motion of the })aper, we see that 
at that moment of time the ball was moving from south to 
north, from west to east, and from up to down ; and from the 
shape of the curves we can determine the position, velocity, 
and acceleration in magnitude and direction of the ball at that 
or any other instant of time : the complete law of the motion 
of the ball is therefore recorded. Should the box be slightly 
tilted and some of the springs elongated or shortened during 
the disturbance, then the motions will not be strictl}- north- 
south, east-west, &c. ; but it is evident that this cannot pro- 
duce any serious discrepancy in the indications miless the 
earthquake motions be exceedingly violent, and when this is 
the case it will not be very difficult to eliminate the errors. 

It is evident the points P and D may be above the ball in- 
stead of below it as in the figure; and this arrangement would 
be preferable when we wish to surround the ball with a liquid, 
as the paper could then be kept quite clear of the liquid. 

Section H. 

Mr. Mallet is of opinion that there is no turning action of th(^ 
ground during earthquakes ; but it is possible this conclusion 
may be perha})S a little premature, since any explanation that 
has been given of the observed twisting of columns, basetl on 
considerations of the attachment at the base, might also a})ply 
to the twisting of rock in its natural position. To test whether 
any such turning action really exists, a simple apparatus, such 
as is shown in fig. 7, might be employed. H J is an iron fly- 
wheel rigidly attached by a stretched thick wire K L to a rigid 
iron framework K M N, or by a thinner wire if lateral motion 
of the flywheel is prevented by a guide. An arm J P carries 
a pencil at P touching a band of paper (the one, for example, 
employed in the previous seismometer) moved by clockwork 
parallel to M N. If the periodic time of the torsional ^ibration 

tJiat may he emploi/ed in Earthqnake Measurements. 49 

of H J be, saj, one fifth of that of the earthquake, then any 
rotatory vibration of the earth will be well recorded*. 

Tlie observations of Mr. Mallet, made at the scene of the 
Neapolitan earthquake of 1857, are of great value in connexion 
with the science of seismometry, which owes its growth in a 
great measure to the labours of that gentleman. But we have 
no hesitation in saying that three recording seismographs, such 
as Ave have described, suitably placed in the plain of Yedo 
and with clocks in telegraphic communication with one an- 
other, would give more information regarding earthquakes in 
a few months than could be obtained by the most ex})erienced 
observers from the remains of many destroyed cities. We are 
aware of the great interest now being taken by the German 
Asiatic Society in the subject of seismometry; and it is to a 
certain extent in consequence of this that we have been led to 
publish this paper. A not very extended series of experi- 
ments would probably be all that would be required before we 
could furnish working drawings of an almost perfect record- 
ing instrument ; and after such instruments had been con- 
structed the Japanese Government might possibly be induced 
to allow them to be used at their telegraph offices. With very 
little extra expense these seismometric records might be sup- 
plemented by regular observations of the natural currents in 
the telegraj)h-lines, to the importance of observing which we 
have recently directed attention in a former paperf. 

Addition, May 1879. 
It is interesting to notice that the principles developed ma- 
thematically in this paper have, since it was written, been 
arrived at by natural selection in the relatively rigid naturally 

* Since wi-iting this paper a ratlier sharp earthquake has been experi- 
enced in Tokio, -w-hich caused the scale-pans of a balance in the Physical 
Laboratory of the Imperial College of Engineers to describe perfect circles, 
the chains" (about 35 centimetres long) which supported the pans and the 
pans themsehes moying like a conical pendulum. The radius of the circle 
described by each pan at the beginning was about 5 centimetres; and the 
motion continued for a long time after the earthquake had ceased. The 
cii'cular motion was probably produced by two successive shocks being 
nearly at right angles to one another. 

Some time after this earthquake we constructed an exceedingly sensi- 
tive rotatory seismograph on the general principle shown in tig. 7, the 
wire K 1, being about ten feet long ; but up t-o the date of one of the authors 
leaving Japan last year the instrument gave no evidence of any earthquake 
producing a turning action by a single shock. 

t " The Importance of a General System of Simultaneous Observations 
of Atmospheric Electricity,'' Transactions of the Asiatic Society of Japan, 
vol. v. part 1, p. 131, and Journal of the Society of Telegraph Engineers, 
vol. vi. p. 242. 

riid. Mag. S. 5. Vol. 8. No. 46. July 1879. - E 

50 l^rof. L). E. Hughes on an Induction-balance 

rapid vibnitorv diapliratrin of the telephone and ])honogra])h 
of Professor Bell and Mr. Edison. For just as the receiving 
diaphragm, from the non-preponderating cliaracter of its 
rcri/ rapid natural vibrations, is able to produce trntlifidly 
in ininiatnre the varied sound-vibrations connnuniwited to the 
transmitting diaphragm, so does our seismograph trnt/ifidli/ 
record in miniature the earthquake shocks it has received. 

And we are led to think that, if rapidity of vibration be com- 
bined with viscous resistance (as explained in the paper) tele- 
})hones and phonographs may be successfully constructed of 
far larger dimensions and of far greater power than has hi- 
therto been attempted. 

V. Induction-balance and Experimental Researches thereicith. 
Bij Prof. D. E. Hughes *. 

[Plate v.] 

IMMEDIATELY upon the announcement of Arago's dis- 
covery of the influence of rotating plates of metal upon 
a magnetic needle (1824), and Faraday's important discovery 
of voltaic and magneto-induction (1831), it became evident 
that the induced currents circulating in a metallic mass might 
be so acted upon either by voltaic or induced currents circu- 
lating in a metallic mass as to bring some new light to bear 
on the molecular construction of metallic bodies. 

The question was particularly studied by Babbage, Sir John 
Herschell, and M. Dove, who constructed an induction-balance, 
wherein two separate induction-coils, each having its primary 
and secondary coils, were joined together in such a manner 
that the induced current in one coil was made to neutralize 
the induced current in the opposite coil, thus forming an in- 
duction-balance, to which he gave the name of " dittbrential 
inductors." In those days physicists did not possess the ex- 
quisitely sensitive galvanometers and other means of research 
that we possess today; but sufficiently important results were 
obtained to prove that a vast field of research would be opened 
if a perfect induction-balance could be found, together with a 
means of correctly estimating the results obtained. In ex- 
perimenting with the microj)hone I had ample occasion to 
appreciate the exquisite sensitiveness of the telephone to 
minute induced currents. This led me to study the question 
of induction by aid of the telephone and microphone : the re- 
sults of those researches have already been ])ublished. Con- 
tinuing this line of inquiry, I thought I might again attempt 
to investigate the molecular construction of metals and alloys ; 
and with this object I have obtained, after numerous compara- 
* Comujunicated bv the Plivsical Sucietv. 


Phil. Mag. S. 5. Vol. 8. PI Y 

Switch - Key 

and Eivpev'iniental Researches thereioitli. 51 

tive failures, a perfect induction-balance which is not only 
exquisitely sensitive and exact, but allows us to obtain direct 
comparative measures of the force or disturbances produced 
by the introduction of any metal or conductor. 

" The instrument now submitted to the Physical Society 
consists, 1st, of the new induction-currents balance ; 2nd, a 
microphone, with a clock as a source of sound ; 3rd, electric 
sonometer, or absolute sound-measurer, a late invention of my 
own ; 4th, a receiving telephone and three elements of 
Daniell's battery. In order to have a perfect induction-cur- 
rents balance suitable for physical research, all its coils as well 
as the size and amount of wire should be equal. The primary 
coils a, a', and the secondary coils h, h\ should be separated and 
not superposed. The exterior diameter of the coils is 5^ 
centims., having an interior vacant circular space of 3 
centims. ; the depth of this flat coil or spool is 10 millims. 
Upon this box-wood spool are wound 100 metres of No. 32 
silk-covered copper wire. I use four of such coils, formed 
into two pairs, the secondary coil being fixed permanently, or 
by means of an adjustable slide, at a distance of 5 millims. from 
its primary ; on the second similar pair there is a fine micro- 
meter-screw, alloAving me to adjust the balance to the degree 
of perfection required. These two pairs of coils should be 
placed at a distance not less than one metre from each other, 
so that no disturbing cause may exist from their proximity. 
The two primary coils are joined in senes to the battery, the 
circuit also passing through the microphone. In place of the 
telephone I have sometimes used a magnetic pendulum, the 
swing or the arc described indicating and measuring the 
forces. I am at present engaged upon a very sensitive volta- 
meter, which shall indicate and measure the force of rigid 
induced currents. The telephone, however, is well adapted as 
an indicator, but not as a measure of the forces brought into 
action. For this reason I have joined to this instrument an 
instrument to which I have given the name of electric sono- 
meter (PI. V.) This consists of three coils c, d, e, similar to those 
already described, two of which are placed horizontally at a fixed 
distance of about 40 centims. apart ; and the communication 
with battery is so arranged that there are similar but opposing 
poles in each coil ; between these two there is a coil, d, which 
can be moved on a marked sliding scale,/, divided into milli- 
metres, in a line with these two opposing primary coils*. This 
central coil is the secondary one, and connected by means 
of a switching key with the telephone in place of the induc- 

* If the coils c and e are of iineqiuil size, the zero of the scale will 
occupy a position similar to that shown on the Plate. 


52 rrol". 1). E. UuglxQS on an Induction-balanee 

tion-l)alanccs. It' this socondaiy coil is near either primary 
coil, we hoar loud tones, due to its proximity. The sameeflPect 
takes place if the secondary coil is near the opposing coil, 
except that the induced current is now in a contrary direction, 
as a similar pole of the primary acts now on the opposite side 
of the induction-coil. The consequence is, that as we withdraw 
it from one coil and approach the other, we must pass a lino 
of absolute zero, where no current whatever can be induced, 
owinor to the absolute equal forces acting equally on l)oth sides 
of the induction-coil. This point is in the exact centre be- 
tween the two coils. 

We thus possess a sonometer having an absolute zero of 
sound : each degree that it is moved is accompanied by its 
relative degrees of increase ; and this measure may be ex- 
pressed in the degrees of the millimetres passed through, or 
by the square of the distances in accordance with the curve of 
electro-magnetic action. If Ave place in the coils of the in- 
duction-balance a piece of metal (say copper, bismuth, or iron), 
we at once produce a disturbance of the balance, and it will 
give out sounds more or less intense on the telephone according 
to the mass, or if of similar sizes, according to the molecular 
structure of the metal. The volume and intensity of sound is 
invariably the same for a similar metal. If by means of the 
switching key the telephone is instantly transferred to the 
sonometer, and if its coil be at zero, we hear sounds when 
the key is up, or in connexion with the wire g, which leads 
to the induction-balance, and no sounds, or silence, when the 
key is down or in contact with the wire Ii, in connexion with 
the sonometer. If the sonometer-coil were moved through 
several degrees, or through more than the required amount, 
we should find that the sounds increase when the key is 
depressed ; but when the coil is moved to a degree where 
there is absolute equality, if key is up or down, then the 
degree on scale should give the true value of the disturbance 
produced in the induction-balance ; and this is so exact that 
if we put, say, a silver coin whose value is 115°, no other 
degree will produce equality. Once knowing, therefore, the 
value of any metal or alloy, it is not necessary to know in 
advance what the metal is ; for if its equality is 115°, it is 
silver coin ; if 52, iron ; if 40, lead ; if 10, bismuth ; and as 
there is a very wide limit between each metal, the reading of 
the value of each is very rapid, a few seconds sufficing to 
give the exact sound-value of any metal or alloy. 

The respective values of the ditlerent metals may, as I have 
already pointed out, be indicated by introducing the sono- 
meter into circuit. I find, however, that it is difficult to 
estimate fractional diiiorences when the sounds to be com- 

and Experimental Researches therewU/i. 53 

pared are loud. I therefore prefer to balance the metal under 
examination bj means of a similar mass placed in the opposino; 
coil, reading on the sonometer the differences of sound, which 
are then slight. Experience has shown that the most accurate 
results are obtained when the sonometer is replaced by a gra- 
duated strip of zinc about 23 millims. wide, 200 millims. long, 
and tapering from a thickness of 4 millims. at one end to a 
fine edge at the other, and superposed in a horizontal plane 
over the opposing coil I/, the metal to be tested being in a 
plane midway between a and b on the left of the plate. 

The delicacy of the readings may of course be greatly in- 
creased by diminishing the angle between the two faces of the 
strip ; but there are many points connected with its use which 
would be too long to describe in this paper. 

As a rule three Daniell elements will be found quite suffi- 
cient ; and even this weak force is so exquisitely sensitive that 
it will find out the smallest fraction of difference in weight or 
structure of metals. Thus two silver coins such as a shilling, 
both qu!te new, and both apparently of the same weight, will 
be found to possess a difference of weight which the instrument 
at once indicates. 

The following experiments will show its exceeding sensitive- 
ness and its wide field of usefulness as an instrument of research. 

I. If we introduce into one pair of the induction-coils any 
conducting body, such as silver, copper, iron, &c., there are 
set up in these bodies electric currents which react both upon 
the primary and secondary coils, producing extra currents 
whose force will be proportional to the mass and to its spe- 
cihc conducting-power. A miligramme of copper or a fine 
iron wire, finer than the human hair, can be loudly heard and 
appreciated by direct measurement, and its exact value ascer- 
tained. AVe can thus weigh to an almost infinitesimal degree 
the mass of the metal under examination : for instance, if we 
take two English shilling pieces fresh from the Mint, and if 
they are absolutely identical in form, weight, and material, 
they will be completely balanced by placing one each in the 
two separate coils, provided that for these experiments there 
is an adjustable resting-place in each pair of coils, so that each 
coin may lie exactly in the centre of the vacant space between 
the primary and secondary coils. If, however, these shillings 
are in the slightest degree worn, or have a different tempera- 
ture, we at once perceive this difference, and, if desired, 
measure it by the sonometer, or by lifting the supposed 
heaviest coin at a slight distance from the fixed centre line : 
the amount of degrees that the heaviest coin is withdrawn 
will show its relative mass or weight as compared with the 
lightest. I have thus been able to appreciate the difference 

54 Prof. D. E. Hughes un an I tiduction-balance 

caused by simply rubbing the shilling between the fingers, 
or the difference of temperature by simply breathing near the 
coils; and in order to reduce this sensibility within reasonable 
limits, I have only used in the following experiments 100 
metres of copper wire to each coil, and 3 cells of battery. 

II. The comparative disturbing value of disks of different 
metals, all of the same size and form of an English shilling, 
and measured in millimetre-degrees, by the sonometer, is the 
following : — 

Silver (chemically pure) 125 

Gold „ „ 117 

Silver (coin) 115 

Aluminium 112 

Copper 100 

Zinc 80 

Bronze 76 

Tin 74 

Iron (ordinary) 52 

German silver 50 

Iron (chemically pure) 45 

Copper (antimony alloy) 40 

Lead 38 

Antimony 35 

Mercury 30 

Sulphur (iron alloy) 20 

Bismuth 10 

Zinc (antimony alloy) (5 

Spongy gold (pure) 3 

Carbon (gas) 2 

III. It will be seen from the above that the instrument 
gives very different values for different metals or alloys ; con- 
sequently we cannot obtain a balance by employing two disks 
of different metals, and the instrument is so sensitive to any 
variation in mass or matter that it instantly detects the dif- 
ference by clear loud tones on the telephone. If I place two 
gold sovereigns of equal weight and value, one in each coil, 
there is complete silence, indicating identity or equality be- 
tween them ; but if one of them is a false sovereign, or even 
gold of a different alloy, the fact is instantly detected by the 
electrical balance being disturbed. The instrument thus 
becomes a rapid and perfect coin-detector, and can test any 
alloy, giving instantly its electrical value. The exceeding 
sensitiveness of this electrical test I shall demonstrate by ex- 
periment, now. Again, as regards coins, it resolves an almost 
magical problem. Thus, if a person puts one or several coins 
into one })air of coils, the amount or nominal value being un- 

and Experimental Researches therewith. 55 

known to myself, I have only to introduce into the opposite 
coils different coins successively, as I should weights in a 
scale, and when perfect balance is announced by the silence, 
the amount in one box will not only be the same nominal 
value but of the same kind of coin. 

IV. We find, by direct experiment Avith this instrument, 
that the preceding results are due to electric currents induced 
by the primary coil, and that it is by the reaction of these 
that the balance is destroyed; for if we take an insulated 
spiral disk or helix of copper wire with its terminal wires 
open, there is no disturbance of the balance Avhatever, not- 
withstanding that we have introduced a comparatively large 
amount of copper wire ; but on closing the circuit the balance 
is at once very powerfully disturbed. 

If the spiral is a flat one, resembling a disk of metal, and 
circuit closed, we find that loud tones result when the spiral 
is placed flat, or when its wire is parallel to those on the coils; 
but if it is held at right angles to these wires, no sound what- 
ever is heard, and the balance remains perfect. The same 
thinor occurs with disks of all non-mao-netic metals, and a disk 
of metal placed perpendicular to the coils exerts no influence 
whatever. The contrary result takes place "with a spiral of 
iron wire or disk of iron: the induced current circulating in 
the spiral is at its maximum when the spiral lies flat or parallel 
with the coils, gi^nng no induced current whatever when at 
right angles; but the disturbances of the induction-balance are 
more than fourfold when perpendicular to the wires of the 
coils than when parallel with the same. This result is simply 
due to the property of magnetic bodies, of conduction of mag- 

V. If we introduce a disk of metal gradually into the 
coils, we find that its powder increases as the square of the 
distance, until it arrives at its maximim^i exactly in the centre 
of the vacant space between each pair of coils, diminishing 
rapidly in the same ratio if the disk be moved towards primary 
or secondary. Thus, in the interior of the coils there is but a 
single line of maximum force ; but at the exterior we have 
on each coil two maxima and one minimmn, the first and 
most powerful maximum being in the centre of vacant space 
between each pair of coils, coinciding with the maximum 
lines of force of the centre of the coils ; the minimum lines of 
force are exactly in the exterior centre of each coil, again 
rapidly rising to a maximum near the exterior edge of coils, 
and gradually diminishing in power from this point. 

If we place exteriorly a bar of metal in the centre line of 
vacant space, w^e find that it has here its maximum disturbing 
power, giving out loud sounds. 

56 Prof. D. E. Iluglies on an Induction-balance. 

11" we now move this bar until it rests on the centre of 
either coil, we find that at this point the bar has no disturbing 
effect whatever, and although the coils at its maximum line 
of force are sensitive to the finest iron wire, a very large mass 
of iron or a rod of 1 centimetre diameter has no disturbing 
effect whatever. Its })aralyzing effects are so remarkable, that 
if we j)lace a fiat piece of iron or other metal across the maxi- 
mum line of force, where loud sounds are given out, the 
instant that this flat piece is moved, so that one or both edges 
touch or end in the minimum line of force, it becomes in- 
stantly neutralized, giving out no sound whatever, notwith- 
standing that a large mass of metal lies in the maximum line 
of force. "We will now demonstrate by experiment the ex- 
ceeding sensitiveness of the induction-balance to the smallest 
piece of metal, if it is in the maximum line of force, and no 
part of it touching the minimum ; and also that by allowing 
either or both ends of this or a very large piece of metal to 
cut or end at the minimum lines of force, complete paralysis 
and consequent silence are produced*. 

VI. There is a marked difference of the rapidity of action 
between all metals, silver having an intense rapidity of action. 
The induced currents from hard steel or from iron strongly 
magnetized are much more rapid than those from pure soft 
iron ; the tones are at once recognized, the iron giving out a 
dull, heavy smothered tone, whilst hard steel has tones ex- 
ceedingly sharp. If we desire to balance iron, we can only 
b.alance it by a solid mass equal to the iron to be balanced. 
No amount of fine wires of iron can balance this mass, as the 
time of discharge of these wires is much quicker than that of 
a larger mass of iron. Hard steel, however, can be easily 
balanced not only by steel but by fine iron wires, and the 
degree of the fineness of these wires required to produce a 
balance gives a very fair estimate of the proportionate time 
of discharge. The rapidity of discharge has no direct relation 
with its electrical conductivity; for copper is much slower than 
zinc, and they are both superior to iron. 

We find that the induction-balance is exceedingly sensitive 
to all molecular changes which take place in all metals sub- 
jected to any of the imponderable forces. Thus we have 
already by its aid studied the effects on metals of heat, 
magnetism, electricity, &c., and of mechanical changes such 
as strain, torsion, and pressure ; and I propose in some future 
paper to describe the remarkable results already obtained, and 
to demonstrate by experiment today to the Physical Society 
the results of these forces upon the induction-balance. 

* This wa* lully demonstrated to the audience bv numerous experi- 

Phil Mag. S. 5. Vol. 8. PI. VI. 



1 , i- 







^ ^r^— ^^, 




1 N?ll. _, 



i 1 




i 1 






\ \ 



i i 

1 1 

1 I 




fn 130 


O rzo 

^ no 

(fi joc 


I \ 


1 / 


' \ 


j / 

1 / 


Z 90 


C 70 


H 60 


KK fci as »7 

96 i 



' \ 1 
V i 

l\ 1 

\ 1 









> no 















' 1 
















V - 






> X. 



1 ^• 

\ ^^^^ 

TIN. ^ 

7-5 a 


^ ' ■ 1 

— ' 

" • 






t:^ t 

i '"v^.^ 1 / 










« 80 7(? 6C S? 4C 30 

Percentages OF THE Metal first nameld m path g^ppiFc 


[ 57 ] 

VI. Note on the Examination of certain Alloys hi/ the Aid of the 
Induction-balance. By W. Cha2sDLER Egberts, F.R.S., 
Chemist of the Mint*. 

[Plate VI.] 

OME weeks since, Prof. Hughes showed me that equal 
volumes of various metals give widely different indica- 
tions with the induction-balance. It appeared probable that 
a careful examination of a definite series of alloys would prove 
to be of interest; and as Prof. Hughes at once gave me the 
most generous assistance, teaching me the manipulation and 
controlling the results, I am able to submit the following ob- 
servations to the Society. 

The relative values of different metals as indicated by the 
induction-balance were given by Prof. Hughes in a paper read 
before the Royal Society on the 15th of May last. They do 
not accord with the values usually accepted as representing 
the relative conductivity of the respective metals ; and this 
being the case, it became important to ascertain what relation 
the indications given by alloys, when under the influence of 
the induced current, bear to their electric conductivities, which 
afforded Matthiessen a basis for dividing them into groups f. 

A series typical of each group was therefore taken ; the con- 
stituent metals were melted together in the requisite propor- 
tions; and the thoroughly mixed alloys were carefully rolled 
to a uniform thickness, usually 1'3 millim. Disks 2-4 millims. 
in diameter w6re then cut with the same punch; and these 
disks were placed in succession on one side of the balance, so 
that their bases lay exactly on a line midway between the pri- 
mary' and secondary coils, this having been found to be the 
plane of maximum force. The respective values of the alloys 
were ascertained either by introducing the sonometer into 
circuit, or by superposing a graduated wedge-shaped scale of 
zinc over the opposing coil of the balance, as has already been 
explained by Prof. Hughes. 

Tlie alloys of Lead and Tin were selected as an example of 
Matthiessen's first group. The results are recorded in the fol- 
lowing Table, and are graphically indicated in the curve No. 1, 
Plate VI. The readings are those of the zinc scale^. 

The Gold-Silver cdloys, representing the second group, pre- 
sented no difficulty of manipulation; and the observations 
were made on disks 1*3 millim. thick and 24 millims. in dia- 

* Communicated by the Physical Society. 

t British-Association Eeport, 18G3, p. 37. 

1 The use of a scale of greater accuracy than the one employed may 
sli,;.^htly alter some of the figiu'es, but it can hardly change the' general 
nature of the curves. 

58 Mr. W. C. Roberts on tlie Kjxtiii'uiation of vertain 

meter. The results are given in the Table and in curve 
No. II. 

'The alloys of Tin and Coi^per^ taken as representative of 
tlie third group, are peculiar. Their tints and fractures are 
widely diti'erent; and the series is interesting as having various 
industrial applications. As many of them are too brittle to roll, 
a block of each alloy 18 millims. square by 7 millims. thick 
was formed with the file. The results are given in the Table 
and on the curve No. III. 




Readings on 




/ 1- 

100 (pure till). 













Sn., Pb 


h5 ' 


36 30 

Sn" Pb 





Sn Pb, 





Su Pb, 




Sn V\ 


I 9. 

(pure lead). 


( 1- 

100 (pure silver). 









99 50 











• 115 








Ag^ Au 




Ag, Au 





■ Ag.j Au 





Ag Au 




Ag Au, 




Ag Au^ 




^g ^"a 






(pure gold). 


( 1- 

100 (pure copper). 



89 00 

Sn Cu,. 




Sn Cujo 




Sn Cu, 





Sn Cuj 




Sn Cu, 








Sn Cuj 





Sn Cu., 




Su Cu' 




Suj Cu 



(pure tin). 


l^otc — The Allovs were not anncnled ; and the temperature was about 
15= C. 

Allocs by tlie aid of tlie laductioii-balance. 59 

If the curves for Lead- Tin and Gold-Silver are compared 
with those given by Matthiessen* for the same alloys, their 
similarity will at once be evident. On the other hand, the 
induction-balance curve of the Tin-Copper series, while bear- 
ing some general resemblance to j\Iatthiessen's curve of con- 
ductivity, differs essentially from it in certain parts. Mat- 
thiessen's curve falls rapidly from 93 (the conductivity of 
pure copper) to 9 (that of the alloy containing 85 volumes 
per cent, of copper). It then passes horizontally in a line which 
is approximately straight to I'd, the conductivity of Tin. 

Some light would appear to be thrown on the ditference 
between the two curves by the work of M. Alfred Richj on 
the density of alloys of copper and tin. He showed that 
copper and tin contract in alloying, the contraction being 
regular from pure tin up to the alloy containing 38 per cent, of 
tin, the density of which is higher than that of pure copper. 
M. Rich's experiments were conducted on allo^-s both in the 
form of powder and ingots ; the latter have alone been given 
in the cur^-e marked with his name on the Plate; and the rela- 
tion between the two curves, especially at the points a, a', h, 
U , is too evident to need comment. 

It may ultimately prove that if the alloys were rolled or com- 
pressed the curve would be modified; and, on the other hand, 
further experiments on the conductivity of the alloys may 
reveal points of identity between the conductivity and induc- 
tion-balance curves ; the part where the former from being 
vertical becomes horizontal would be especially worth exami- 
nation. It may be well to point out that the alloys SnCug 
and SnCu^, which occupy critical positions on the induction 
curve, have been shown by M. Rich to be singularly free from 
the disturbing influence of liquation. 

The work would appear to be interesting as showing that 
the induction-balance may afford a simple means for detecting 
variations in the molecular structure of alloys and for indica- 
ting allotropy in metals with greater accuracy than has hitherto 
been possible. 

Practical ap2:)lication. — The possibility of ascertaining the 
standard fineness of alloys by the aid of electricity long ago 
occupied the attention of physicists. In 1823 M. Becquerelf 
suggested that trustworthy indications might be afforded by 
the electromotive force developed when the alloy is placed in 
an exciting fluid, together with an alloy of known composition. 

* Op. cit. p. 46, aud Watts's Dictionary of Chemistry, vol. iii, p. 943. 
t Ann. de Chimie et de Phys. tome xxx, 1873. 
X Ibid. t. xxiv. p. 343 (1823). 

()0 Mr. 0. Heavisidc on the 

The sul)jcct was partially invcstifrated by CKrstod in 1828*; 
and as its practical importance was further indicated by Gay- 
Lussac in 18301, 1 made a series of expez'iments in order to 
ascertain how far the more delicate appliances in use at the 
present day could be made available. The results, however, 
were not entirely satisfactory. 

Prof. Hno;hes's Induction-balance rendered it possible to 
resume the research on a new basis. It is only necessary to 
glance at such a curve as that of the Gold-Silver series No. II. 
to be satisfied of the probability that certain parts of it, at least, 
would indicate minute differences of standard. I would there- 
fore direct special attention to the series of alloys which He 
between pure silver and silver alloyed with 5 per cent, of 
oold. These are shown in a separate curve, where the scale 
of percentages is more extended. Such alloys as Nos. 2 to 6 
are known to refiners as dore ; and No. 2 contains less 
than 2 grains of gold to the pound troy, a quantity which 
could not be extracted with profit by the ordinary operation of 
'' })arting." Small as the amount of precious metal is, its 
presence is clearly indicated on the induction curve, as are 
also the larger amounts of gold contained in Nos. 3-5. 

Experiments are in progress on other series which promise 
to afford trustworthy indications ; but of course the establish- 
ment of a method of verifying the composition of alloys of 
the precious metals nmst in part depend on the degree to which 
the presence of traces of foreign metals influence the accuracy 
of the results. 

My object in these notes is not to insist on any particular 
application, but to bear testimony from a metallurgical })oint 
of view to the delicacy and simplicity of the instrument 
which Prof. Hughes has placed at our disposal ; and I would 
offer him my sincere thanks for the liberal aid he has so readily 
given me. 

VII. On the Theory of Faults in Cables. 
By Oliver Heaviside. 
1. ri"^HE only kind of fault to be here considered is either a 
J- local defect in the insulation, or an artificial connex- 
ion between the conductor of a cable and the earth. When 
a fault occurs in a submarine cable, its most manifest effect 
on the working is to increase the strength of current leaving 
the sending end, because the resistance is reduced ; while at 
the same time the strength of current arriving at the distant 
* Ann. de Chimie et dc Phijs. t. xxxix. 1828, p. 274. 
t Inst nut ion stir I'Essai dcs Matures (PArt/od par hi I'viv JIuiuidc. 
I'aris, 1830. 

Theory of Faults in Cables. '61 

end is reduced, the loss of current through the fault being 
greater than the increase in the current leaving the sending 
end. Another effect is to increase the speed at which signals 
can be made through the cable. A cable may be considered 
electrically as a long cylindrical condenser, or as a conductor 
having a great number of condensers of small capacity con- 
nected at equidistant points to it on the one side and to earth 
on the other. When an electromotive force is applied at one 
end, to establish a permanent current in the circuit these con- 
densers have to be charged, an operation requiring time for 
its fulfilment; and before the current can cease when the elec- 
tromotive force is removed, the charge must be got rid of : 
in fact, the current results from the discharge of the cable's 
electricity. If there is a fault, the discharge of the cable is 
facilitated; for there is not only a smaller quantity of electri- 
city to be discharged, but more paths are open to it. Similarly 
the charging of the cable is facilitated, as will be seen by sup- 
posing the cable when uncharged to contain two exactly equal 
and opposite charges. Let one of these discharge itself. The 
cable will then become charged with the other ; and since the 
discharge of the first is facilitated, the charging of the cable 
by the second is also facilitated. With a fault, a smaller 
quantity of electricity is required in order to produce the per- 
manent state of electrification when an electromotive force is 
applied at one end of the line than when there is no fault ; 
therefore, other things being the same, a given fraction of the 
final permanent state is more quickly reached in the former 
than in the latter case. Similarly the effect of a given signal 
is more rapidly dissipated in the former than in the latter case; 
and consequently from both these causes signals can be packed 
more closely together when the cable is faulty ; or, in other 
Avords, the speed of working can be increased with equal 

2. Before preceding to the mathematics of the subject, I 
give some of the calculated arrival curves in simple cases. 
Referring to fig 1, suppose in the first place the cable is per- 
fectly insulated and free from charge, and that both ends are 
to earth. At a given time ^ = 0, introduce a constant electro- 
motive force E at one end P of the cable. Then the well- 
known curve of arrival of the current at the distant end Q is 
represented b}' curve 1. Time is measured to the right, and 
current strength upwards. The unit of time is 

ckP , ckP 

ilogaO = 

where / is the cable's length, and c, Ic its cajiacify and resistance 


Mr. 0. lleuviside on t/ic 

per unit of IcMioth. For ;i cable 2()()0 miles long, with c = }^ 
niicroi'arad, and /: = () ohms, we have cki- = H seconds, ami 
a = "list)!) sec. The current, though calculahle from the first 
instant, is relatively insi'usihle for some little time. Thus, 
when t= l-5a, it has only reached '0047 of its final strength, 
but, thereafter increasing much more rapidlv, reaches half its 

final strength in (Ja, -1)8 in 20a, and its final strenffth -- after 
the lapse of a theoretically infinite time. 






^^^Hh/^." '^.^'^ 


Now compare curve 1 with curve 3. In the latter all the 
circumstances are the same, with the exception that there is a 
fault of infinitely small resistance situated at the middle of 
the cable. Of course such a fault could not be worked tln-ougli, 
since no current would arrive at the receiving end. Never- 
theless this is not by any means a case of an unpractical 
nature; for it is quite possible to work, and very well too, a 
cable containing a tault of 7u\i-t to no resistance. It will be 
seen that with the fault of no resistance the current becomes 
sensible sooner, and increases much more rapidly. It reaches 
•0017 of its final strength in 1«, -044 in U, -1318 in 2«, "4274 
in 3«, •G8 in 4ei, •8v)57 in 5a, and •i>82(5 in Sx. Half the final 
strength is reached in 3"3«, as against Got with no fault. 

When the fault has a finite resistance the arrival curve of 

the current is intermediate between curve 1 and curve 3. 

The one shown by curve 2 corresponds to the case of a fault 

having a resistance equal to one fourth of the cables. This 

makes the final strength of current = one half its value 

when there is no fault. In 2« the current reaches "0420 of 

Theory of Faults in Cables. 


its final streugth, half its final strength hi 4-7«, and -1)840 m 


3. Now, referring to fig. 2, suppose both ends of the Ime 
to be insulated, and the cable free from charge. At any time 
^ = let a small charge be instantaneously communicated to 
one end of the cable. This corresponds to working with con- 
densers at both ends when the capacities of the tenmnal 
condensers are verv small, and terminal resistance negligible. 
The charge thus communicated then diftuses itself along the 
cable, becoming finally equally distributed. Sir W. Thomson's 
mathematical theory indicates that the potential at_ any point 
.V rises in exactly the same manner as the current rises at the 
same point when both ends of the line are to earth and a con- 
stant electromotive force operates at one end. Therefore the 
arrival curve of the potential at the distant end in working 
with condensers at both ends is the same as the arrival-curve 
of the current shown by 1, fig. 1- It is reproduced in 1, fig. 2, 
for comparison with the curves for a fiuilt. 

Fisr. 2. 

When there is a fauU, or merely general loss through the 
insulator, there is conductive connexion between the conductor 
and earth ; consequently the charge initially communicated 
to the beginning of the line must ultimately all escape, reducing 
the potential everywhere to zero. Therefore, although the 
current as shown by curve 1, fig. 1, never reaches its full 
streuo-th, yet, since insulation is never absolutely perfect, the 
potential, as shown by curve 1, fig. 2, must sooner or later 
reach a maximum and then fall to zero. As the leakage in- 
creases, the time taken to reach the maximum decreases. Tlie 
maximum is reached in 10-3a, as shown by curve 2, fig. 2, 
when there is a fault in the middle of the line of one fourth 


Mr. 0. Iloaviside on the 

the resistance of the latter ; and with a fault in the middle of 
infinitely small resistance, the maximum is reached in &boi, 
as sliown by curve 3, fig. 2. It cannot be reached sooner 
with a single fault. 

4. In condenser working, the working current is the current 
ent(>ring the receiving condenser — that is, the rate of increase 
of its charge, and therefore proportional to the rate of increase 
of the potential at the insulated receiving end when terminal 
resistances and capacities are neglected. The arrival-curve of 
the current when there is no fault is shown in fig. 3, curve 1. 
This curve was given by Sir W. Thomson in 1854, not how- 
ever in connexion with condenser working (for that method 
was not then invented), but as showing the current at the dis- 
tant end jiroduced by an infinitely short contact with an infi- 
nitely powerful battery at the beginning, both ends being kei)t 
to earth. The current reaches a sensible proportion of its 
maximum much more rapidly than without condensers. It 
reaches its maximum in 3*l)3a, and then decreases. 

With a fault of infinitely small resistance in the middle of 
the line, other things being the same, the arrival- curve of the 
current is shown by 3, fig. 3. It reaches '0081 of its maxi- 
nnmi in Soi, '0523 in la, and its maximum in 2-()a nearly. 
It then falls to zero, which it reaches in 6'5a, and becomes 
negative, as the electricity runs back to escape through the 
fault to earth. 

Curve 2, fig. 3, is similar. It corresponds to the fault in 
the middle having one fourth the cable's resistance. The 
maximum is reached in 3*45a, and zero in 10'3«. 

Ficc. 3. 

Theory of Faults hi Cables. 65 

5. The influence of a fault on the amplitude of reversals 
may be readily calculated. In the first place, -n-ithout con- 
densers. Let contacts, alternately + and — , be made with 
a battery at the beginning of the line, while the distant 
end is to earth. If the reversals are sufficiently ra,pid, the 
resulting received current is nearly a simple harmonic function 
of the time. Let c be the capacity and h the resistance per 
unit of lenorth of cable of leno-th /, having a limit in the middle 
of resistance zkl. Also let t be the period of a wave, or the 
time occupied by a pair of contacts. Then the maximum 
strength F of the received-current waves is 



^^^^ (e« + £-« — 2 cos n)-i / e" + e-" + 2 cos n 

1 1 ") "^ 

+ 75 — (e''-e-" + 2sinn)+-r-y-:5(e" + e-" — 2cos?0 } , 
where n = A /__, and E is the electromotive force of the 

battery. Or, approximately, 


Here — is the current that would be produced in the line if 
perfectly insulated, and permanent contact made with the bat- 
tery. -^ e~" is the reversal-factor, and ( I + i^ h ^ •> •> ) 

the fault-factor. Now, if Tq is the greatest current possible 
with the fault, 

r= ^ 


therefore F . , 

where -i . I 


+ ^ 

9 2 

2nz %irz 


and d){n) is the reversal factor. ^^ represents the proportion 

of the maximum received current which is arrived at by the 
PMl Mag. S. 5, Vol. 8. Xo. 46. July 1879. F 

66 Mr. 0. Heavisidc oii the 

reversals, or, for brevity, the proportional amplitude. If c= i, 

P = 

/, 2 2* 

V 1 + - + - 

V n n- 

Let n = 10, which would make the time t of a pair of contiicts 
T= - — 2— =l'347a, where a is the unit previously used ; then 

^ Vl-22 

Thus the fault increases the proportional amplitude for this 
speed d>-2, per cent. If z = ^}^^^ and « = 10, then p is rather 
more than 6; and a fault of infinitely small resistance makes 

6. Now for condenser workino;. Let every thing be the 
same as in the last paragraph, with the addition of a condenser 
of capacity r^cl at the sending-end and another of capacity 
i\cl at the receiving-end, i\ and r^ being extremely small. 
We shall now have 

^ E 16nV2 

The fault-factor is the same as before ; and if the maximum 
received current possible were also the same as before, we 
should arrive at exactly the same conclusions as regards the 
influence of the fault on the proportional amplitude of the re- 
ceived current. But the comparison is here faulty, since 




is the maximum current possible with both ends to earth, and 
the condensers do not allow the received current to reach such 
a strength, except in the imaginary case of condensers of in- 
finite capacity ; for a condenser of infinite capacity is mathe- 
matically equivalent to a conductor of no resistance if there 
is no difference of potential between the coatings to start with, 
or to a battery of no resistance and electromotive force E if 
there is a dift"erence of potentials E. But, as is shown later 
on, the maximum strength of the recei^"cd current with con- 
densers becomes proportional to 



Theory of Faults in Cables. 67 

when z is very small ; so that for a fault of small resistance 
the same results follow as before for its effect on the propor- 
tional amplitude. 

7. Since the proportional amplitude is increased by the 
fault for the same speed, a higher speed is obtained with the 
same proportional amplitude. Thus, with the ends of the 
cable to earth, as in paragraph 5, if n^ is the value of n when 
there is no fault, then, to have the same proportional amplitude 
with a fault of resistance zJcl in the centre, we must increase n 
to «2j so that 


1* 1 

l-\ h - — 

2n2Z S7il 

Now the speed is inversely proportional to r, and therefore 
directly proportional to w" ; therefore the percentage increase 
in the speed is 



ForWi = 8, 9, and 10 we shall find 92^=9-7, 10-7, and 11-7, 
and the increase in the speed 47, 41, and 37 per cent., if 
^=^•2, which would make the greatest possible received cur- 

For a fault of no resistance, ^^=0, and 

With ni = 8,9, and 10 this gives »2=10-2, 11-3, and 12-4 ,- 
and the increase in the speed is 62, 57, and 53 per cent. These 
values of ??i, namely 8, 9, and 10, are chosen on account of 
their nearness to the values in the working of long cables. 
The corresponding values of t are 2"10, 1*66, and 1*34«. 

8. When a natural fault, or local defect in the insulation 
is developed in a cable, it tends to get woi'se — a phenomenon, 
it may be observed, not confined to cable-faults. Under the 
action of the current, the fault is increased in size and reduced 
in resistance, and, if it be not removed in time, ends by stop- 
ping the communication entirely. Hence the directors and 
officials of submarine-cable companies do not look upon faults 
with favour, and a sharp look-out is kept by the fault-finders 
for their detection and subsequent removal. But an artificial 
fault, or connexion by means of a coil of fine wire between 
the conductor and sheathing, would not have the objectionable 


68 Mr. 0. Heavisidc on the 

features of a natural fault. If |)roporly con.structcJ it would 
be of constant resistance, or only varyin;^ with the toin])era- 
ture, would contain no electromotive force of })olarization, 
would not deterioiMte, and would consideral)ly accelerate the 
speed of working. The best position for a single fault would 
be the centre of the line; and perhaps ^ of the line's resistance 
would not be too low for the fault. 

9. In the cable, the potential v at any point x has to satisfy 
the differential equation 

rf'u , dv ..-. 

dP='^dt^ (^> 

and the current at x is 

^ k dx 

Tlie particular solutions in paragraphs 5 and 6 regarding the 
strength of the received current when reversals are made with 
a battery at the sending-end are derived from the simple har- 
monic solution 

v = e' (A cos +Bsm)( h -r- I 

+ 6 ' (A'cos +B^sm)( yj 

of the above equation (1). When there are faults, each of 
the sections into which they divide the cable has a solution of 
the above form. In the case of a single fault, thei*e are four 
conditions (namely, two for the fault and one for each end of 
the line) which suffice to determine the eight constants. But 
to determine the maximum strength of the received current, 
it is only necessary to find the sum of the squares of two of 
the constants. This shortens the labour, which is again greatly 
shortened by neglecting e"" in comparison Avith 1. 

10. The calculation of arrival-curves demands an entirely 
different method of proceeding. The general problem may be 
thus stated. Given a cable with faults in it, also the con- 
nexions at the ends, resistances, condensers, &c., and given 
also the electrical state of the whole system at a certain time : 
to find its state at any time afrer, the system being left to 
itself, and the action of the known laws regulating the poten- 
tial, current, &c. In fig. 4 let P Q be a cable, of length /, resist- 
ance k, and electrostatic capacity c per unit of length. Also, 
let the tei'minal connexions be as shown, viz. at the begin- 
ning P a resistance R^ and a condenser of capacity Ci shunted 
by a resistance Si, with a similar arrangement at the end Q. 
This includes the cases of signalling either with or without 

Theory of Faults in Cables. 69" 

condensers, shunted or unshunted, at either or both ends. Let 
the signalling be from P to Q ; then E^ is the battery resist- 
ance, and Eg the receiving-instrument's resistance. Let the 
electromagnetic capacity of the latter be L. Further, let 
there be n faults of resistances Zj, Zg, ... at distances x^ 
from the beginning P, "where .^'=0. 


Fig. 4. 



At the time t = let the potential of condenser Ci be Vi, 
and Yg the potential of Cg. Further, let \ = f\x) be the po- 
tential of the line when < = 0. Since we have taken into account 
the magnetic capacity of the receiving-instrument, the speci- 
fication of the initial state of the system is not complete unless 
we know the current in Eg when t = 0. Let this be G. Then 
we want to know r, x\, v^, and g at time t, where v, Vi, V2, and 
g are what V, Vi, Yg, and G then become. 

11. BetAveen any two faults let the initial potential be ex- 
panded in a convergent series of the form 

SA sin f^ + h\ 

This can be effected in an infinite number of ways. Then 

XAsmr-^ + b\€-"T^, (2) 

where T = ckP, satisfies the partial differential equation (1), 
and will therefore represent the potential at time t between 
the same limits, provided the sets of constants A, a, and b are 
so determined as to make (2) satisfy the conditions imposed 
by the presence of the faults and the terminal connexions. 
This, of course, can be done only in one way. 

At each of the faults two conditions are imposed. First, 
the potential must be continuous at the fault ; secondly, the 
current in the line going to the fault on the left side exceeds 
the current growing from the fault on the right side by the 
current in the fault itself from the conductor to earth ; and 
the latter is, by Ohm's law, equal to the potential of the line 
at the fault divided by the resistance of the latter. 

Let Yoj-^ be the initial potential between cV=0 and x = ,ri, 
y^iTo between a' = A-i and x=j'2, and so on. Then the first 

70 Mr. 0. Heavisidc on the 

condition is satisfied at all the faults if 

Vo., =2 As 



/ax , \ 

Y.,r,=yor, + ^Bsm <'\'''\ • 

V..3 = V.,., + 2:Csin^^^V^' 

. (3) 


and so on. Tlic second condition is satisfied at all the faults 
by making 

P A,- . /UiXi , , \ 

and so on, where ^ Z 

12. The terminal arrangements have next to be considered. 
By the theory of the condenser, at the beginning P ^Ye have, 
at time t, 

_Vi p di'i _Vi—v_ 1 dv 
~Wi~^'di~~U^ ~~kd^' 
Hence, if 

El • Si Ci 



''^^Fr '''=d' 

we have 

i'i = r — mj 



as the relation between the potentials of Ci and the beginning 
of the line, and 

= t'-(wi + ni)r-^ +7?iriP— 2-?;!i»i;-iZ=^-^3 . (o) 

as the equation to be satisfied by the potential at .i'=0. 
At the end Q we have 

1 dv 1-2 , ^ dv2 

kdx~'^~ ^2'^^^ dt' 


V-Vo = fjUz + lj-^. 


Theory of Faults in Cables. 71 

Therefore if 

Ivo bo Cg Ll 

12 ^-2 ^2 

n.->— ~, ?-o= -f, 5 = 

we have 

r2 = i- + /»2^— +sP^3, .... (8) 

giving 1-2 in terms of i" at x = /, and 

= i- + Cm.2 + no)/ -y- + n^r-Jr j-., + (s + m.2r2n^)l^ — ^ 

H-n^^vZ^g ... (9) 
as the condition held by the potential at x=-I. In (5), (8), 
and (9), for -^ has been substituted —f -:f—i' 

13. Xow the law of formation of the a's and 6's can be 
found. From .'f=0 to x = Xi, 

To^,=2Asin(y +6j; 
and from the last fault at .'f=.r„ to x = l, 

Y^j = SA sin f y + ?M + 2B sin ^ ^ ^^ 

+ 2,0 sm -^— 1 h . . . . 

Inserting the first of these in (5) and the second in (9), and 
then making .t" = in the first case and x = l in the second, we 

tanZ.^=^^^ + ^^^^^^-^"^^^^'^^S . . . (10) 

sin (a, + i.) + q. sin a. ^ 1 - y'^ + </;' sin a. (l - y' ^ + ?;" sin a^ ^1 - :^\ + . 

cos (a,- + ^/,) + 9.' cos a, [l - ~ j + ^'; cos a,. ^ 1 - "-^J + yl" cos a,- (^1 - ^M + , 
_ _ (ms + "o)^', — (« + *ra2?i2»2)«f + ^2^2-5ai . ^ ^ N 

~ i-/i2?-2a? ' ' ' ' ' y ) 


Equations (10) and (11) serve to determine the a's and Z/'s. 

14. Now onlv the A's remain to be found. This is to be 

72 Mr. 0. Heaviside on the 

efiected by an integration along the lino from .r = to .?•=/, 
with a similar process applied at P and Q to the potentials of 
Ci and Cj and the current in Rg- Collecting the expressions 
for the separate divisions, wo have, from .r = to A' = .ri, 

Vo,;=-SA,sin(^+^)=SA,.M;,say; .... (12) 
from x = a.\ \o a' = X2, 

=2A.M",say; . (13) 
from .r = .r2 to .r = .r3, 

V,,X3 = 2A,| sm {^-j- +h,)+q'.sm '^ ^ 

+ 5;'sin'^i^:^^]=2A,M7,say; . (14) 

and so on to the end of the line. 

At the beginning P, by (4) we have 

Vi = XAi(sint,— rnia,.cos6i) = 2A.K!, say. . . . (15) 

At the end Q, by (8) we have 

Va = 2A,- [ I sin (a. + h) + q. sin «,• ( 1 " 7 ) 

+ g':sin«.^l-^2)+... j +(wja,-.^af) I cos («. + ?>,) 

+ ^;cosa,(l-l^ij+^;'cosa,(|l-Y) + ...}] 

= 2A,N;', say (16) 

Also, let V3 = GH; then by (6), 

V3 = 2 A ..r - « . I cos (a . + h^ + q\ cos a, (l - ''^ j 

+ ^;'cos«,(l- ^^) + . . . } =:^A,N';', say. (17) 

To find A,-, the ith value of A. Multiply both sides of each 
one of the last equations, (12) to (17), by the coefficient of A,- 
in that particular equation ; e.g. multiply (12) by M|, (13) by 
Mp and so on. Next integrate each side belonging to the 
line between the limits for which it is true. Thus (12) from 
A'=0 to x—x^^, &c. Apply a similar process to V,, Vj, and 

Theory of Faults in Cables. 73 

V3 by multiplying them by r^l, r^l, and si re pectively. Finally 
add together all the results, right and left sides respectively, 
excepting for V3, which must be subtracted, and then equate 
the two sums. The result is 

+Y,r,m',+N,r,w-Y^sm":J'^ { rXM:M;,cf^ 

i'=0 I. Jo 

+ r%M';M;;dr+ r'A,M;"M;:f/.f+...+ViZN;.N;, 

+ A^'J^'lsl-k,sm:^i\^ (18) 

It Avill be found, on making the substitutions in (18) of the 
expressions for the M's and K's, and effecting the necessaiy 
reductions, that in the summation on the right-hand side of 
(18), the complete coefficient of every one of the A's vanishes 
identically, by reason of equations (10) and (11), except for 
A- ; whence 

V„^M:/f^ + V.,.,M;w.r + . . . + Y,r,m\ + Y,r,lK: 

\ M yx + \ Mi'hlv + ... + rJW,' + rgZNf 2 _ slW/'^ 

.... (19) 

This completes the solution; and the state of the whole 
system is determined for any time t. 

15. When the initial potentials Vo^i &c. of the line in the 
different sections are given explicitly as functions of x, the 
sum of the integrals in the numerator of (19) may be WTitten 

pVo..sin(^ +b^clt+ fV.,.,y:sin ^^^-^~''''^ Z.z; 

There is a great simplification when the initial state of the 
system is, not arbitrary, but such as would be finally produced 
by a constant electromotive force E acting at P (fig. 4). Then 
the complete numerator of (19) reduces to 


74 Mr. N. D. C. Hodges on the Size of Molecules. 

for any numbor of faults and for all the terminal arrangements 
that can bo made out of those shown in tig. 4. The denomi- 
nator of (19) is a function of a^ and i,. Thus 

A,= 5^; (20) 

[To be continued.] 

VIII. On the She of Molemles. By N. D. C. Hodges*. 

IF we consider unit mass of water, the expenditure on it of 
an amount of energy equivalent to 636*7 units of heat 
will convert it from water at zero into steam at 100°. I am 
going to consider this conversion into steam as a breaking-up 
of the water into a largo number of small parts, the total sur- 
face of which will be much greater than that of the water 
originally. To increase the surface of a quantity of water by 
one square centimetre requires the use of '000825 metre- 
gramme of work. The total superficial area of all the parts, 
supposing them spherical, will be 47r r^ N, the number of parts 
being N. The Avork done in dividino- the water will be 47r 
r^ N '000825. For the volume of all the parts we have -^tt 
r^ N. This volume is, in accordance with the requirements of 
the kinetic theory of gases, about -^^q of the total volume 
of the steam. The volume of the steam is 1752 times the 
original imit volume of Avater. Hence — 

fTrr^N 3000 = 1752 

47r;'2N '000825 = 636-7423 

One unit of heat equals 423 units of work. 

Solving these equations for r and N, we get r = "000000005 
centimetre, a quantity closely corresponding with the previous 
results of Sir AVilliam Thomson, Maxwell, and others ; and N 
equal 9000 (million)^, or for the number in one cubic centi- 
metre 5 to 6 (million)'*. 

Around every body there is an atmosphere of more or less 
condensed gases. On the surface of platinum these must be 
neai'ly in the liquid condition, as shown by the power of })lati- 
num to bring the atoms of oxygen and hydrogen so near 
together that they combine. These vapours on the surface 
have a tendency at ordinary temperatures to expand; and part 
of them can do so, if the surface of the body is reduced. There 
is in those condensed atmospheres an explanation of all the 
phenomena of superficial tension. The energy in the unit of 
area ought to be equal to the work done in compressing a 
* Communicated bv the Author. 

On a neio Fonn of Spectrometer. 75 

quantity of the vapour from the gaseous to the liquid state 
sufficient to cover the surface a few molecules deep. The mo- 
lecular attraction seems to be very slight in gases, where the 
molecules are ten or fifteen molecular diameters apart. To 
get some idea of the amount of work done in compressing one 
gramme of oxygen to the liquid state, we mav consider that in 
the union of one gramme of hydrogen with eight grammes of 
oxygen 34,462 units of heat are produced. It matters not 
that the condensation is brought about by the energy of che- 
mical separation rather than by the work done in pressing 
them together in a cylinder. 

The supei-ficial energy of platinum is 169"4 metre-grammes 
per square metre, or "OIGQ^ per square centimetre, equal to 
"00004 of a unit of heat. The proportion 
9 : 34,462 = A- : '00004 

gives the weight of water condensed on one square centimetre 
of surface, or the volume in cubic centimetres as '00000001, 
which is the thickness of the layer, or diameter possibly, of 
the molecules. 

Physical LalDoratorv, Harvard College, 
May 14; 1879. 

IX. On a ncic Form of Spectrometer, and on the Distribution 
of the Intensif)/ of Light in the Spectrum. By JoHX Wil- 
liam Draper, 2I.D., President of the Facidty of Science in 
the University of New York*. 

I HATE invented a spectrometer which, I think, opens a 
new and interesting field to those who are engaged in 

The ordinary spectroscope is occupied with the frequency 
of aether-vibrations or wave-lengths. That which I am about 
to describe has a different fimction. It deals ^yith the in- 
tensity or brilliancy of light. It depends on the well-known 
optical principle that a light becomes invisible when it is in 
presence of another light about sixty-four times more brilliant. 

In some researches published by me in 1847, on the pro- 
duction of light by heat, or the incandescence of bodies, I used 
this method as a photometer, and became sensible of its value. 
The memoir in which those experiments are related may be 
found in my recently published ' Scientific Memoirs,' page 

Having also published in 1872 a memou'on the distribution 
of heat in the prismatic spectrum, and sho^vn that the course 
* Communicated bv tlie Author. 

76 Dr. J. ^V. Draper on a neiv 

of its incroasinff intensity from the more to tlie less refrangible 
regions is due to the comj)ressioM of the coloured sj)aces that 
corres])ondingly takes place, owing to the action of the })rism 
itself, but having failed to obtain satisfactoiy measures in the 
case of the diffraction-spectrum (in which such comj)ression or 
condensation does not occur), 1 was led to reflect whether 
better success might not be secured by attem])ting to measure 
the relative intensity or distribution of light. 

Admitting what is commonly received as true, that the 
yellow is the brightest of the coloured spectrum s])aces, and 
that the luminous intensity diminishes from that in both di- 
rections above and below, I supposed that, if such a spectrum 
Avere brought into the ])resence of an extraneous light, the 
illuminating power of which could be varied at j)leasure, after 
the red and the orange on one side, and the green, blue, indigo, 
and violet on the other, had been extinguished, the yellow 
would still remain in the midst of the surrounding illumination. 
On making the experiment it turned out differently. 

For the sake of clearness of description I will call this ex- 
traneous light, from the functions it has to discharge, the ex- 
tinguisJimg ligld. 

There are many different plans by Avhich the principle above 
indicated may be carried into practical effect. Several of 
these I have tried, and have found the following a convenient 

Eemovc from the common three-tubed spectroscope its 
scale-tube, and place against the aperture into which it was 
screwed a ])iece of glass ground on both sides. In front of 
this arrange an ordinary gas-light, attached to a flexible tube, 
so that its distance from the ground olass may be varied at 
pleasure. On looking through the telescope, the field of view 
will be seen uniformly illuminated, this being the use of the 
ground glass. The brilliancy of the field depends on the dis- 
tance of the gas-light, according to the ordinary photometric 

1. Case of the Prismatic or Dispersion Spectrum. 

If the extinguishing light be for the moment put out, and 
in the proper place before the slit-tube the Inminoiis flame of 
the Bunsen burner that accompanies theapparatus be arranged, 
on looking through the telescope a spectrum of that luminous 
flame will of course be seen. The slit itself should be very 
narrow, so that the spectrum may not be too bright. 

Now let the extinguishing flame be placed before the ground 
glass, and a spectrum is seen in the midst of a field of light, 
the brilliancy of Avhich can be varied at pleasure. If. this ex- 

Form of Spectrometer. 11 

tiiio-uishing flame be at a suitable distance, the whole spectrum 
may be discerned. As that distance is shortened, tirst the 
violet and then the other more refrangible colours in their 
descending order disappear, and at length in the steadily in- 
creasing effulgence the red alone remains. The yellow never 
stands out conspicuously, as might have been expected. 

This is scarcely consistent with the assertion that the yellow 
is the brightest of the rays. The red is plainly perceptible 
lono- after the yellow has gone. There is a greenish tint 
emitted by gas-light that disappears a little previously to the 
extinction of the red. 

From these observations I think that the luminous intensity 
of the coloured spaces has a relation to the compression or 
condensation that the prism is impressing upon them. It 
may be that, properly considered, the intrinsic intensity of 
the light is the same for all. In this we must always bear in 
mind the physiological peculiarities of the eye. 

The foregoing statement is perhaps sufficiently explicit to 
enable any one to verify the facts. I may, however, mention 
some improvements in the apparatus, which experience has 
led me to adopt. 

The intensity of the extino-uishing light may be insufficient 
to obliterate the spectrum even though the slit be closely nar- 
rowed. How, then, may the intensity of the spectrum be 
diminished, and that of the extinguishing light be simul- 
taneously increased ? I accomplished this by depositing on 
that face of the prism which acts as a reflector an excessively 
thin film of silver. This, though it was to the transmitted 
rays quite transparent, increased very greatly by its metallic 
reflection the extinguishino- ones. I could not see any dif- 
ference between the spectrum of the light that had coma 
through this film and that before the face was silvered, but 
the reflected light was incomparably more brilliant. The 
complete obliteration of the entire spectrum presented now no 

Xothing need be said about collateral contrivances, which 
would suggest themselves to any one. A strip of wood a metre 
long and bearing divisions, served to keep the extinguishing 
lamp in the proper direction as regards the ground glass, and 
indicated its distance. I may add, however, that satisfactory 
observations can be made very conveniently by keeping the 
extinguishing flame at a constant distance, and varying its 
intensity by opening or closing the stopcock. This avoids the 
trouble arising from moving it. In one instrument I caused 
an index attached to the head of the stopcock to move over a 
graduated scale^ and so ascertained how much it was opened. 

78 l^r- J. W. Draper on a neio 

This, tliouoh permitting of pleasant working, had not the ex- 
actness ol' the method of distances. 

Such are the results obtained from the prismatic dispersion 
of "-aslight. I completed this part of the investigation hy an 
examination of sunlight. For this purpose I resorted to the 
fore(Toin(T principle, introducing a beam of sunliglit reflected 
from a heiiostat through a slit. The spectrum of this was 
thrown u[)on a paper screen, so placed that by opening or 
closin<T an adjacent window-shutter the light of the sky in 
greater or less quantity could fall upon the paper, and act a? 
an extinguisher. When the shutter was fully opened, the 
spectrum was quite obliterated; and on gradually closing it so 
as to diminish the extinguishing light, the red region first 
came into view, the other colours following in the order of 
their refrangibility, the extreme violet appearing last. On 
reversing the movements of the shutter the colours disappeared 
in the reverse order, the red disap})earing last. 

At the moment when the red was approaching extinction 
there always existed on its more refrangible side a gleam of 
greyish-green light. In was in the position of that greenish 
gleam which appeared, as I have described, when gaslight 
was examined. Its colour recalled to my mind the faint 
oToenish-grey light I had seen when a strip of platinum was 
icrnitedby a feeble electric current, as described in my memoir 
of 1847, above referred to. 

Subsequently I constructed a camera having two apertures 
in its front. Through one of them (by a suitable arrangement 
of a heiiostat, slit, direct-vision prism, and convex lens) a solar 
spectrum was formed on the ground glass. Through the 
second aperture, mIucIi was about an inch square, covered with 
a o-lass ground on both faces, an extinguishing beam of sun- 
lioht passed. This ground glass served to disseminate the 
extinoruishing light uniformly over the spectrum. I could 
reo-ulate its power by varying the size of the aperture through 
which it came, by means of a slide. 

It is needless to give details of the results obtained by this 
instrument. They were identical with those described in the 
foregoing paragra})hs. 

It miglit be supposed that the irrationality of dispersion of 
diflFerent prisms would influence the results perceptibly. 
Accordingly I tried prisms of different kinds of glass and 
other transparent substances, but could not find that this was 
the case. h\ all the extinction began in the violet and ended 
in the red. 

Nor did there seem to be any difference when the effect 
was viewed by different eyes. To all, irrespective of age or 

Form of Spectrortieter. 79 

the condition of their sight, the extinction took place in the 
same manner. I had not an opportunity of examination in a 
case of colour-blindness. 

2. Case of the Grating or Diffraction-spectrum. 

If the cause of the increasing intensity of light, in the 
prismatic spectrum, from the more to the less refrangible 
region, be the compression exercised by the prism on the 
coloured spaces, increasing as the refrangibility is less, we 
ought not to find any such peculiarity in the diffraction- 
spectrum. In this the coloured spaces are arranged uniformly 
and equally in the order of their wave-lengths. An extin- 
p-uishino- lio-ht ouo-ht to obliterate them all at the same 

Having modified the common three-tube spectroscope, as 
has been described, I put in the place of its prism a glass 
grating inclined at 45° to rays coming in through the slit. 
The ruled side of the grating was presented to the slit. Now, 
when the extinguishing flame was properly placed before the 
ground glass, the plain side of the grating reflected its light 
down the telescope-tube. In this, as in the former case, the 
spectrum was seen in the midst of a field of light, the intensity 
of which could be varied by varying the distance of the ex- 
tinguishing flame, or by varying the opening of its stopcock. 
This lio-ht needs no reinforcement bv increasing the reflectino- 
power of the back face of the grating, these spectra being 
much more feeble than those given by a prism, and the un- 
assisted light being quite able to extinguish them. 

As the glass grating I was using gave its two series of 
spectra of unequal brightness, I selected the most brilliant, 
and in it used the spectrum of the first order. I saw, not 
without pleasure, that as the force of the extingtiishing illu- 
mination increased, all the coloured spaces yielded apparently 
to an equal degree, and disappeared at the same moment. 
Sometimes, however, there seemed to be a very slight dif- 
ference in favour of the red. On diminishing the illumination 
all the colours came into view, apparently at the same time. 
This spectrum gives a better opportunity than the prismatic 
for observations on the yellow space, which, by being uncom- 
pressed, exposes a wider surface to view. This yellow space 
showed no superiority in resisting extinction over the other 

But as gaslight compared with sunlight is deficient in the 
more refrangible rays, I repeated the examination of the 
latter, as I had previously done for the prismatic spectrum, 

80 On a neio Form of Spectrometer. 

moJifjinoj tlie apparatus so as to use a grating in place of the 
prism. The observations in this case of sunlight were quite 
as satisfactory as those in which gaslight bad been used. 

General Conclusions. 

1st. In the prismatic spectrum the luminous intensity in- 
creases from the more to the less refrangible spaces, its 
maximum being not in the yellow but in the red. This is due 
to the action of the prism, which narrows and as it were con- 
denses the coloured spaces more and more as we pass towards 
the red, increasing the intensity of the light as it does that of 
the heat. 

2nd. In the grating or diffraction-spectrum the luminous 
intensity is equal in all the visible regions, all the colours 
being simultaneously obliterated by an extinguishing light. 

It must however be borne in mind that these conclusions 
should be taken in connexion Avith the physiological action of 
the eye. Owing in part to the imj)orfect transparency of its 
media, and partly to the inability of its nervous mechanism to 
transmit waves of certain frequency to the brain, the spectrum 
does not begin and end sharply, as to a perfect eye a perfect 
spectrum ought to do. 

There are hence two causes which must not be overlooked 
in these observations. 1st, the physiological peculiarity of 
the eye, which gives to each end of the spectrum the aspect 
of gradually fading away ; 2nd, in the case of solar light 
the absorption action of the atmosphere, which is chiefly ex- 
erted on the more refrangible rays. 

I think, bearing in mind the correlation of light and heat, 
both being corresponding manifestations of the same vibrating 
movement in the icther, that these results substantiate those I 
published in 1872 on the distribution of heat in the spectrum, 
and that as the different coloured spaces are equally luminous, 
so they are equally warm. 

I have made some attempt to compare with each other the 
luminous intensity of the bright lines in various spectra, 
especially those emitted by a strontium-flame ; but not being 
able to continue these researches at present, I have postponed 
them to a more favourable opportunity. 

University of New York, 
May oth, 1879. 

[ -^1 ] 

X. Litellii/enct' and Miscellaneous Articles. 

T HAVE the honour to present to the Academv a pattern of elec- 
-*- trie burner reduced to the simplest form possible. The two car- 
bons are maintained parallel by two insulated copper tubes separated 
by an interval of 2 or 3 millims.. in which they slide with friction, 
and which serve at the same time to direct them and to bring the 
current. They are surrounded by a directing circuit composed of 
five or six helices coiled upon a tliin rectangular frame 40 centims. 
in length and 15 centims. wide. I have explained how this circuit, 
traversed by the same current as the carbons and in the same 
direction, brings and fixes the electric arc at the extremity of the 

The lighting takes place automatically. For this purpose the 
two extremities of the carbons are wrapped round with a thin 
caoutchouc band, which presses them to one another ; a small piece 
of iron wire is then insinuated between them, or a little above, 
which puts them into communication at one point only. As soon 
as the circuit is closed the current passes through this wire, makes 
it red-hot, and melts the caoutchouc ; the two carbons, having 
agaiii become free, separate, aud the arc is set up -nith a sort of 
explosion. Carbons can be employed of any size up to S millims. 
diameter. At this limit the wear does not exceed 8 centims. per 
hour. As it goes on, the points approach the supporting tubes ; 
but they can be from time to time brought back to their initial po- 
sition by sliding the carbons in the tubes by a common movement, 
without extinguishing them. In future applications an easily de- 
vised mechanism will perform this office ; and as M. Carre manu- 
factures carbons the length of which reaches 1 metre, the lamp can 
remain lighted during twelve hours, which exceeds all needs. It 
will be remarked that the carbons are not separated by any insula- 
ting material, that it is not necessary to first break off their points, 
nor to fix them at their base, nor to furnish them at their point 
with any inflammable material ; they are used just as they come 
from the maker's. It is sufficient to introduce them into the tubes 
which are to support them, and to leave them to the directing action 
of the outer circuit. In reahty there is no candle to construct ; there 
is only a sort of wick to place, which burns all alone to the end. 

The apparatus can be suspended in two ways — either with the 
points above, or directing them towards the ground. These are 
very different conditions. Let us study the first case. 

The electric arc cannot, without breaking, exceed a length de- 
pending on the intensity of the current. Between two horizontal 
points it should be rectilineal, because, according to the laws of 
conductiAity it takes the shortest path, and tends to return to it 
when forced to deviate, in virtue of a sort of elasticity. But it is 
deranged by the ascending currents of air occasioned by its heat ; 
and that is why it takes a curved form. It is also deranged, and 
much more energetically, by the directing circuit. These two a-c- 
tions join in bending it upwards until equilibrium is established 
between them and its elasticitv ; but they also combine to lengthen 

Fhil. Mag. S. 5. Vol. 8. No. 46. July 1879. G 

82 Intelliyence and Miti:celUuu'oug Arliclt'ti. 

it, and to diminish at the same time its resistance to breaking and 
the intensity of the current. It is evident that if tliey cooperate to 
fix the light at the summit of the carbons, it is on the condition of 
lessening the extreme length the arc can attain, or, what is the 
same thing, the number of foci that can be kept alight with a given 

It is no longer so when the points are turned towards the ground. 
While the arc tends to ascend along the carbons, the directing cir- 
cuit drives it back, lowers it, and lodges it between the points, dis- 
tant from 7 to 8 millims. The two actions, whieh before were 
added together, are now subtracted one from the other ; and so far 
from lengthening the arc, they shorten it; instead of diminishing 
its resistance to rupture, and lessening the intensity of the current, 
they augment both. The arc may be said to be as it were com- 
pressed between two opposite actions: it is shorter, narrower, less 
expanded, more dense, and consequentl}'^ hotter ; and the numlx^r 
of the foci can be augmented. M. Jabloschkoff's candles, in other 
respects so well combined, have nevertheless the inconvenience that 
the points are directed u])wards. The arc produced by them ha,s 
a natural tendency to bend and raise itself ; and the same tendency 
is impressed upon it by the electromagnetic action exerted upon it 
by the current, which ascends in one carbon and descends in the 
other — an action identical with that of my directing circuit, though 
less energetic. The burner A\ith the points below must therefore 
excel those candles. In fact this is proved by experience. AVith 
a machine hardly sufhcieut to light three of those candles 1 can 
easily maintain five burners armed with much bigger carbons, each 
giving about twice as much light ; and as the points are immersed 
in the mass of the arc, they acquire a more vivid brightness and an 
incomparably whiter tint. Six foci, even, can be lighted ; but they 
give a less sum total of light than five ; if we double the number 
we lose in quantity. It is always so when the electric light is 
divided beyond measui'e : the division must be purchased by a 
proportional loss. 

The management of these burners requires careful study. When 
the points are above, the lighting is very difhcidt, because imme- 
diately it is produced the force of the directing current projects it 
strongly upwards, that force being proportional to the square of 
the intensity. When this increases, it becomes absolutely impos- 
sible to light the carbons ; one can get only a vast flame which 
immediately disappears with a noise. If the current is less intense, 
the light continues, but much spread out, very tall, and always 
very noisy, on account of the amplitude of the oscillations which 
take place at each inversion of the current. Finally, the equili- 
brium is not at all stable. If an accidental current of air comes 
for a moment to augment the height of the flame, nothing can 
restore it, the limit of its elasticity is passed, and it soon breaks. 
In the burners with the points beneath, the lighting is easy, and 
the equilibrium stable : for if a movement of the air or a deficiency 
of the current causes the arc to ascend, it settles between the two 
carbons at the place where they have not been thinned by combus- 
tion ; it lodges in an interval not exceeding 2 or ;i millims. Far 

Intelligence and Miscellaneon^ Articles. 83 

from lengthening, it shortens ; instead of decreasing, its resistance 
to rupture and the intensity augment : and the light gently re- 
descends to resume and keep its place at the extremity of the car- 
bons. If, on the contrary, the current should increase, the arc 
bends and becomes concave towards the carbons : but, its tendency 
to ascend counterbalancing the action of the directing current, it 
never stretches enough to break. The best economic conditions 
are attained when this curve is just pronounced enough to prevent 
the ascensional movement of the light. In this case the unavoid- 
able noise of the electric light is reduced to its minimum, because 
the amplitudes of the vibratory motion are the smallest possible. 

In brief, the burner which I submit to the Academy, with its 
points beneath, reahzes considerable advantages: — (1) that of sim- 
plicity, since it needs no mechanism and requires no preliminary 
preparation ; the whole amounts to a suppoi't and some carbons : 
(2) that of mechanical economy, since the number of the flames is 
almost doubled ; (3) increase of light, since each of the new foci 
is nearly twice as effective as the old ones ; (4) the quality of the 
light, which is whiter ; (5) a more advantageous disposition of the 
foci, which direct their greatest sum of light downwards, where it 
is of use, instead of losing it skywards, where it would be useless : 
(6) lastly, economy of the combustible, since in proportion to the 
size of the carbons the consumption is less. All this constitutes 
for the electric light a sensible advance, and cannot fail to enlarge 
the place it has already taken in public lighting, thanks to the 
improvement of the engines, to the carbons of M. Carre, and to M. 
Jablosclikoff's candle. — Comptes Rendus de T Academic des Sciences, 
April 2S, 1879, t. Ixxxviii. pp. 829-832. 




The divergences between the two theories stand out most clearly 
when the moments with which a current-element tends to rotate 
an elementary magnet are determined according to both. Accord- 
ing to the electromagnetic theory, the current-element rotates the 
magnet out of the plane when both stand perpendicular to the line 
joining them and are situated in the same plane ; while according 
to Ampere it cannot act at all upon the elementary ciurreut equiva- 
lent to the magnet, since it stands peii)endiculav to every part of the 
latter and at the same time to the connecting lines leading to them. 

If the current-element falls into the connecting line, according 
to the electromagnetic theory it exerts no rotating action upon the 
magnet ; but according to Ampere it sets the equivalent elementary 
current continuously rotating about its axis — an action which is 
quite foreign to the electromagnetic theory. 

If the magnet lies in the direction of line of conjunction, a cur- 
rent-element perpendicular to this, according to both theories, 
rotates the magnet out of the plane, but according to Ampere's 
theory with a moment twice as great as according to the electro- 

84 liitiUnjencc and MisceUaneuu.s ^[rlicles. 

For closed circuits tin: differences coini)cnsate one another, hiil 
the parts which tlie individual elements of the circuit have in the 
lotal action are different. Thus, according to the electromagnetic 
theory the elements of the vertical circuit of a tangent-compass 
all act with equal detlecting force upon the very short needle ; 
accoi'ding to Ampere the elements situated in the vertical diameter 
exert no action, while those in the horizontal diameter act twice as 
powerfully as according to the other theory. 

In the memoir the electromagnetic is compared with the general 
electrodynamic theory, which also assumes transversally-acting 
forces, and was de\ eloped by the author in his memoir " On the? 
Fundamental Formulas of Electrodynamics,'' published in vol. lix. 
of the Sitzumjsherkhte of the Academy (18G9). 

The comparison has refei'ence, first, to the forces, and, secondly, 
to the pairs of forces, which a current-element exerts upon an ele- 
mentary current. In the former respect Ampere's theory, and all 
those which also assume transversal forces, though of such a nature 
that they cannot move the common centre of gravity of two cur- 
rent-elements, agree with the electromagnetic theory. In the 
second respect the electromagnetic theory corresponds only with 
(rrassmann's. But as these two theories differ in the expressions 
for the forces, there is not any electrodynamic theory containing 
in itself the electromagnetic. With the exception of Grassmann's, 
all the theories contain, though not in like manner, continuous ro- 
tations of the magnets by the action of the component of the 
current-element in the connecting-line. — Kaiserliche Akademic der 
Wissrnscliaften in Wien, mnth.-natunc. Classe, April 17, 1879, pp. 

110, 111. ■ 


In this note we are informed that the amalgamated barium easily 
obtained by Crookes's metkod, by digesting solution of barium 
chloride with sodium-amalgam, does not after distillation contain ain/ 
jinrc hariam at all, but leaves o«^/ anamahjnhi rich i)i barium, which 
may contain (52-77 per cent, of mercury. 

It was already mentioned by Bunsen that the barium- or calcium- 
amalgam that appears at the amalgamated platinum electrode in the 
electrolysis of aqueous solution of chloride of barium or calcium 
respectively, also obstinately retains mercury. 

In all probability S. Kern's method, viz. heating oxide and iodide 
of barium with sodium, extracting with quicksilver, and distilling, 
will yield no better result. All the statements about the fiilvt'ci/- 
ii'hite metallic lustre of barium must evidently be referred to the 
amalgam. Pure barium, as obtained by Bunsen and Matthiessen 
by electrolysis of the fused chloride, is bronze-coloured. This colour, 
it is true, is sometimes exhibited by the most superficial layers of 
the barium-rich amalgam, which under the action of a very elevated 
temperature ha\e been deprived of mercury ; but even such por- 
tions of the amalgam are grey on the inside, and in water they 
leave considerable traces of mercury. — Kai^erl. Akad. d. ]\lsse»sch. 
i}i Wien, math.-naturiv. Classe, 1879, Xo. X. p. 109. 







AUGUST 1879. 

XL Electro-optic Observations on various Liquids. By JoHN 
Kerr, LL.D., Free Church Training College, Glasgow*. 

IN two short papers "svliich were published some years ago, 
I showed how I had succeeded in inducing a power of 
double refraction in glass, carbon disulphide, and several other 
dielectrics, by the application of electric forcef. In this paper 
I propose to ofiPer some notes of a later and more extended 
series of experiments on the same subject. The methods 
applied are, for the most part, much the same in principle now 
as formerly ; but my means of observation have been greatly 
amplified and improved, chiefly by assistance from the Govern- 
ment Fund. I begin with the construction of the most im- 
portant part of the apparatus. 

1. New Plate Cell. — This piece is represented in the adja- 

cent diagram. It is made of a block of carefully selected 

* Communicated by the Author. 

t " On a new Relation between Electricity and Liglit," Philosopbical 
Magazine, November and December 1875. 

Phil. Mag. S. 5. Vol. 8. No. 47. August 1879. H 

86 Dr. J. Kerr'.s Elect ro-oplic 

plate glass, I of an incli thick, 8 inches long, and originally, 
for convenience in boring, about 4 inches wide. The first 
step in the construction is made with steel drill and turning- 
lathe. Two fine holes, about j^^ of an inch wide, are drilled 
right through the block, one ])arallel to its length, and the 
other crossing the ibrnier at ritrht an<rles in the centre of the 
piece. Each of the borings is parallel to, and ecpiidistant 
from, the two plate-faces. 

The plate is now reduced to a more convenient width, one 
inch of it (as it stands in the diagram) being ground away at 
the top from end to end, and similarly one inch at the bottom, 
except that a piece wivh sensibly square section is left project- 
ing below the plate, round the vertical boring as axis. The 
plate is also made to taper at each end, as in the diagram, 
though this is not essential. 

Two other borings are now made, each through the })late, 
at right angles to the plate-faces. One is a tunnel, concentric 
with the plate, shaped as in the diagram, about an inch in 
heit];ht, and ^ inch in width, and leaving a POod maro;in of 
polished plate-surface all round its mouths ; the other is a 
slightly tapering hole through the projecting piece mentioned 
above, into Avhicli is fitted afterwards a stopcock of glass, 
which is easily Avorked by hand so as to open and close the 
vertical boring. The sides of the tunnel are carefully finished ; 
they are sensibly plane, and perpendicular to the long boring 
and to the plate-faces. In these and the following operations, 
the polish of the plate is preserved with care, for which pur- 
pose the surfaces are permanently guarded by a shell of hard 

The electric terminals within the tunnel are two balls of 
brass, originally spherical, and a quarter inch in diameter. 
Two thin shafts of brass pass from the ends of the block through 
the long borings, and are screwed firmly into the balls. Round 
the outer end of each of the sliafts is a pierced plug or washer 
of india-rubber ; outside of this is a perforated disk of brass, 
of rather smaller diameter than the washer, and well rounded, 
Avhich moves freely along the shaft ; and outside of each disk 
is a brass ball of ^ inch diameter, which screws onto the end 
of the shaft. To provide for the insertion of conducting wires 
into these outer balls, two fine holes are bored through each 
of them, along diameters perpendicular to each other and to 
the shaft. The outer balls are screwed along the shafts until 
the washers are veiy strongly compi-essed. To prevent all 
possibility of leakage at the junction of inner balls and block, 
each of the long borings has been widened a little at the inner 

Observations on various Liquids. 87 

end into a conical funnel ; each of the inner balls also has been 
backed by a zone of lead. 

At this stage of the construction, when the small spheres 
Avere seen to be sjmimetrically and securely placed in the 
tunnel, they were taken out, and very carefully flattened in the 
turning-lathe, so as to present approximately plane but still 
well rounded faces to each other ; and they were then electro- 
plated with a shell of silver as thick as writing-paper. As the 
balls lie Anally in the cell, their least distance from each other 
is exactly ^ inch. 

The cell is closed by two panes of the finest plate glass, 
about -jJg inch thick, and 2 inches square, which are simply 
kept upon the plate faces of the block by pressure. The press 
is made of tAvo small planks of mahogany, shaped as shown 
by the dotted lines in the diagram, and connected at the corners 
by four square-headed screw-nails, each proA^ided with a bat^s- 
tail nut ; but in working the cell, I find two diagonally oppo- 
site screws quite sufficient in most cases. Between the planks 
and glass are two thin sheets of india-rubber cloth, these, as 
well as the planks, being channelled neatly in continuation of 
the tunnel. 

The whole piece is supported by two fine pillars of glass, 
which are firmly fastened to the block by coils of silk thread. 
The pillars terminate below in a solid wooden stand. When 
the cell is in position on the experimental table, the two faces 
of the plate of liquid are vertical, and the axis of the electric 
field, or the straight line joining the centres of the inner balls, 
is horizontal. 

The supporting pillars, as well as the ends of the cell-block, 
are covered with a thick shell of lac varnish. 

I think that I have now mentioned everv thins essential to 
the cell, except a small stopper of glass, which, at the beginning 
of each experiment, is dropped into the mouth of the vertical 
boring. It prevents the entrance of stray particles of dust, 
and is of use also in restraining evaporation when the cell is 
charged with a very volatile liquid. This plate cell is far 
superior to the old one described in the second of my former 
papers ; it gives finer optical effects, and is ever so much more 
easily handled. 

2. Working of the Cell. — To charge the cell with a liquid, I 
always use a small filtering funnel drawn out into a fine end, 
which passes along the upper boring, quite through the roof 
of the tunnel, leaving a narrow surrounding space for escape 
of air. When the charge of liquid is found to be not suffi- 
ciently clean, the cell is emptied at once by turning the lower 
cock, and is then charged again from the bottle as before ; and 


88 Dr. J. Kerr's Electro-optic 

a good many repetitions of this operation are sometimes re- 
quired before tlie cliarf^e is sensibly free from specks of solid 

Wben tlie coll has to be cbarfred -witli a new liquid, the 
press is unscrewed, tbe planks and panes are removed, tbe 
faces of tbe block are cleaned, two clean panes are laid against 
the mouths of the tunnel, and held there while the cell is 
thoroughly rinsed with a proper solvent. The j)anes 
are removed, the faces of tbe block are again cleaned, two 
clean panes are placed as before, and tbe rinsing is re- 
peated. Half-a-dozon thorough rinsings with ether and alco- 
hol are generally suthcient to prepare the cell perfectly lor any 
new liquid. 

3. Optical Compensator of Strained Glass. — In the follow- 
ing experiments, 1 require continually to introduce definite and 
very faint birefringent actions at some point between polarizer 
and analyzer. The pieces which I employ for this purpose 
are perfectly rectangular slips, all cut out of one carefully 
selected plate of glass -j\; of an inch thick, and all of the same 
dimensions, width | of an inch, length 7 inches. When such 
a slip is extended, it acts upon the transmitted light as a posi- 
tive uniaxal with axis along the line of tension ; and when it 
is compressed it acts as a negative uniaxal with axis along 
the line of compression. These optical actions are in most 
cases very definite and sensibly pure, though perhaps never 
perfect as the actions of good natural crystals. 

4. Hand Compensator. — This is one of the slips (3), worked 
by hand in the manner described in my former papers. It is 
held between the first and second Nicols, immediately in front 
of the latter, with its faces perpendicular to the ray, and its 
length inclined at 45° to the plane of polarization. Kept 
steadily in position, it is strained by an effort of hands or fin- 
gers at each end, the axes of the couples applied being parallel 
to the ray, so that one edge of the slip is extended and the 
opposite edge compressed. According to the statement already 
maile in (3), tlie extended and compressed parts of the slip act 
respectively as positive and negative uniaxals with axes parallel 
to the edges. When the glass is chosen with ordinary care, 
and preserved from any considerable changes of temperature 
during the observation, these optical actions are (to sense) 
perfectly pm-e, tension of one slip being always totally neutra- 
lizable by parallel compression or perpendicular tension of 
another slij). 

5. Fid-ed Compensator. — Tliis is one of the standard slips 
(3), M'hich hangs freely in a constant vertical position from a 
purposely constructed stand. To give the required effect of 

Observations on various Liquids. 89 

double refraction, the slip is simply stretched along its length 
by weights attached to its lower end. The arrangements for 
this piece were somewhat troublesome, but not such as to re- 
quire a particular description. There is no cement used in its 
construction. The glass is attached to the stand above, and to 
the weights below, by double bands of thin leather, which are 
folded on the two ends of the slip, and kept adherent to the 
glass by small blocks of wood and light clamping-pieces of 
brass. The fixed compensator thus constructed acts very well 
up to a, tension of sixteeir pounds ; and beyond this I have not 
yet gone. 

6. Arrangement of the Pieces. — -The optical effects obtained 
are sensibly modified by very small changes in the source of 
light, and in the positions of the pieces ; but I shall not dwell 
upon these variations here, as they were noticed at some length 
in the second of my former papers. In all cases, the acting- 
ray is horizontal, undeviated through its whole course, and 
about a foot distant from the table which .supports all the 
pieces. Of the various arrangements tried, the following is, 
I think, the best upon the whole. The diagram shows all the 
pieces in horizontal section through the ray LM, L being the 
source of light, and M the observer's eye. L is a flat parafhn- 



flame presented edgeways ; P is the polarizing Nicol ; A is the 
dielectric cell (1), having its outer balls connected by copper 
wires, one with the prime conductor and the other with earth ; 
B is a couple of stationary compensating plates of glass (3), 
hanging vertically, and mounted so as to admit of the attach- 
ment of stretching weights to one or the other or both (5) ; C 
is a neutralizing plate which is sometimes required in mea- 
surements and in the more delicate observations ; Q is the ana- 
lyzing Xicol. The distance PQ is from 40 to 60 inches. The 
hand compensator is not shown in the diagram ; when used, 
it is held between the pieces C and Q. 

7. Conduct of cm Observation. — The pieces are brought most 
conveniently into the line LM in a certain order of succession. 
The piece first placed is the polarizer P : it is laid carefully 
with its principal section at 45° to the horizon — that is, at 45° 
to ^^hat is afterwards the axis of the electric field. The ana- 

90 Dr. J. Kerr's Electro-optic 

lyzer Q is then laid so as to suit the observer's eye, and is 
turned into the position of perfect extinction ; nnd this being 
done, tlie two Nicols are left untouched, if possible, till the 
end of the experiment. The cell A, with concbicting wires led 
from its outer balls to ])rime conductor and earth respectively, 
is now put in position under direction from the observer, 
who sits at the polariscope, and restores the light by the use 
of the hand compensator. When A is well ])laced, the line 
LM is perpendicular to the platc-fiices of the cell, and the 
object restored by the hand compensator is a fine streak of 
light, })assing midway between the balls in the cell, and pro- 
jecting well above and below them. When this has been done 
once for all, the cell is left unmoved throughout the experi- 
ment. The fixed compensator B, containing either one plate 
or two, is now placed care fully, so that the line LM passes through 
the centre of each plate in a direction perpendicular to its faces. 
The last piece C is not required always, but only when the 
purity of initial extinction in the ])olariscope has been in any 
degree lost by the introduction of A or B ; it is a piece of com- 
mon })late, the more irregular in temper the better, about ^ of 
an inch thick, fixed in a movable stand ; its modes of application 
and action are precisely the same as those of the larger neu- 
tralizing ])late described in my first paper. AVhen things have 
been thus arranged, the cell is charged with clean liquid (2), 
the observer sits at the polariscope, and, the initial extinction 
being still unimpaired, the electric machine is set in motion. 

Definite Chemical Compounds. 

8. Carbon Dlsidpldde as a Dielectric. — My first trial of 
the new cell was with this liquid, which is much the 
best dielectric yet discovered. The arrangements and i)roce- 
dure are exactly as described in the last two articles; the cell 
is charged with perfectly clean carbon disulphide, and the 
initial extinction is perfect. A small movement of the machine, 
one turn or less, gives a very fine restoration of the light in 
the polariscope. As the potential rises, the light increases 
steadily till it is quite brilliant ; but if a spark be taken upon 
the knuckle from the prime conductor at an}' point in this 
process, the phenomenon vanishes instantly. 

9. Character of the Optical Effect. — The preceding experi- 
ment is repeated, with the addition of the hand compensator 
(4). The compensating slip is put in position with its length 
horizontal, and the initial extinction is found to be unimpaired ; 
the light is then restored steadily by electric action, and the 
slip is successively stretched and compressed with forces in- 

OOservations on various Liquid>>. 91 

creasing continuously from zero. Horizontal tension is found 
to strengthen the effect of electrical action in every case, while 
horizontal compression, with similarly perfect distinctness and 
regularity, ^A'eakens the effect down to sensibly pure extinction. 
"When the electric action is feeble, a certain small compression 
of the compensator extinguishes the electrically restored light 
as a whole, or simultaneously in all its parts ; but when the 
action is intense, the axal part of the field requires a greater 
compression than the outer parts, and the extinction-pheno- 
mena take the form of two dark bands, which will be particu- 
larly described immediately. 

When the plane of polarization of the light rendered bv the 
first Xicol is either horizontal or vertical, either parallel or 
perpendicular to the lines of force, and the second Xicol is at 
pure extinction, the effects of electrization are evanescent ; if 
they do appear, they are irregular in character and trifling in 

There is certainly no rotation of the plane of polarization in 
the present case: for when the light restored by electric force 
is tried by small rotations of the second Xicol in contrary di- 
rections from the position of initial extinction, it is found to 
be similarly and equally affected by the two movements. 

The action of dielectrified carbon disulphide upon trans- 
mitted light is therefore similar to that of glass extended in a 
direction parallel to the lines of force : it is a sensibly pure case 
of what is known in optics as a tiniaoxdli/ hirefringent action, 
the axis being paj-a//^/ to the lines of force, and the action 
positive. Of two component vibrations, which are polarized 
in planes respectively parallel and perpendicular to the lines 
of force, the latter is relatively retarded. 

10. Carbon Disulphide as an Insulator. — To test the insula- 
ting power of this and other liquids, I compare the strikino-- 
distance of the prime conductor when the wire connectiuo- it 
•with the cell is in position and out successively. When the 
cell is charged Avith carbon disulphide the result is decisive. 
All the pieces being placed as in the experiments just de- 
scribed, the machine is worked at an ordinary rate, and sparks 
are drawn from the prime conductor on the knuckle, or on a 
metallic ball connected with earth ; the Avire from prime con- 
ductor to cell is then removed, and sparks are again drawn 
from the prime conductor now simply insulated. 1 have seen 
very little perceptible difference (if any) between the two 
cases, the sparks being of much the same density and leno-th 
when the connecting wire is in position and when it is out. 

I present this fact prominently, because it has an important 
bearing on the interpretation of the electro-optic experiment 

92 Dr. J. Kerr's Electro-optic 

(8). It M'onld be rash to assert that there is no considerable 
discharf^c of electricity throufrh the cell in tl)o course of that 
experiment. On the contrary, I think that when the wires 
are in position and the machine working, there is a certain 
quantity of convective discharge throu<ih the liciuld. Dut the 
])res(Mit observation shows, to a certainty, that the shell of bi- 
sulphide in the cell, though not more than one eighth of an 
inch thick, is able to keep the two inner balls at a large 
difference of potentials, a larger difference than would be 
supported under similar conditions by more than an inch of 
air. The litjuid is therefore a good insulator ; and the resto- 
ration of the light by electrization is due, in all probability, to 
electrostatic inchictive action through the liquid. Up to this 
point I haye merely giveu a revision of observations made long 
ago with the old plate cell, and published in the second of my 
former papers. 

1 1. Ed'lindion-hands in CSj. — Tlie cell is charged with clean 
carbon disulphide, and the pieces all stand as in the diagram 
of (G), the ])rincipal section of the first Nicol being inclined 
at 45° to the horizon, and the second Nicol being at pure ex- 
tinction. The correctness of the arrangements is tested by a 
repetition of the electro-optic experiment with the liand com- 
pensator (9). Matters being thus arranged, I begin now by 
attaching a weight of some pounds, say eight or nine, to one 
of the fixed compensating slips B ((>). The experiment begins 
thus with a strong permanent restoration from extinction in 
the polariscope, the restoration being due to vertical tension 
of glass, which is here optically equivalent to horizontal com- 
pression of glass, and therefore optically contrary to the 
electric action (9). It should be remembered that the object 
now restored in the polariscope is a fine vertical streak of 
flame-light, passing through the centre of the electric field, 
not encroaching on either ball, but ])rojecting well above the 
balls, and also well below. Things being thus prepared, the 
observer sits at the polariscope, and the machine is worked at 
a moderate rate. 

The first thing observed is a broad horizontal band, very dim 
and ill-defined, which crosses the flame in the axal part of the 
electric field. As the potential of prime conductor and induc- 
tric ball rises, the band comes out more and more definitely, 
and darkens by degrees till it is perfectly black, every trace of 
that part of the flame having disappeared. As the potential 
still rises the flame begins to reappear in a faint speck or patch 
at the centre of the band. The patch brightens and widens 
gradually till the one band along the axis is clearly broken up 
into two, lying symmetrically on opposite sides of the axis, 

Observations on various Liquids. 93 

and concave to each other. As the potential still rises, the 
bands move symmetrically outwards from the axis, dividing 
the flame into three large segments which are sensibly of equal 
brightness. And when the electric action is at the strongest, 
near spark-discharge through the liquid, the bands cross the 
flame at points very little, if so much as, outside of the cylin- 
der Avhich envelops the two balls. The bands are still in- 
tensely black and well-defined where they cross the flame; and 
they are quite distinct in their whole course, as fine arches 
resting on the two balls, and spanning the intermediate field. 
When the machine is stopped, and the potential falls to zero 
more or less slowly, the optical effect passes through the same 
phases, but of course in reversed order. 

12. This fine experiment presents a case of what is known 
in optics as the cross duplication of positiA^e uniaxal plates, 
the axis of the compensating slip being vertical, and that of 
the liquid plate horizontal. The birefringent action of the 
dielectric plate is not uniform either in time or space, but 
increases in time at any given point of the field as the po- 
tential rises, and diminishes at each instant regularly in space, 
outwards from the axis of the electric field; and this con- 
sideration affords a sufficient general explanation of the form 
and phases of the phenomena. When the flame is divided 
by the bands into three segments, the light of the middle 
segment is restored by predominance of electric action in the 
liquid plate, while the light of the extreme segments is still 
restored by ]Dredominant action of the compensating plate of 
glass. 1 think the following variation of the experiment 
worth mentioning as an additional illustration of this vicAv. 

The extinction-bands being formed as in (11), and kept 
stationary in the outer parts of the electric field by constant 
motion of the machine, I introduce the hand compensator, and 
apply a horizontal compression beginning at zero. As the 
compression rises gradually to a large intensity, the arched 
bands move in gradually towards the axis of the field, until 
they coincide in one band, which finally disappears. If the 
compression be suddenly relieved at any point in this process 
the arches come into view again at once in their old positions. 
Like efiects are obtained by a strong downward pull upon the 
weight which is attached to the fixed compensator, 

13. These extinction-bands, obtained by electric action 
against the tension of the fixed compensator, improve in all 
respects with every increase of tension and correspondino- in- 
crease of potential. Against a tension of one pound or two 
the bands are moved into the outer parts of the field by a 
comparatively feeble electric action, and they are wide and 

94 Dr. J. Kerr's Electro-optic 

dim and not well defined, although they present all the essen- 
tial features of the pheuonionon clearly enough ; but against 
a larger tension of twelve pounds to sixteen, the bands are 
beautifully distinct, narrow, sharply defined, and ver^' black. 
Sonic elementary electro-optic measurements with this litpiid 
will be described afterwards ; in the meantime I shall merely 
ask the reader to notice the large range of measurable optical 
effect here obtained, and with such a small cell, from a ten- 
sion of one pound or less in the fixed compensator up to a 
tension of sixteen ])ounds. 

14. Benzol (C,;H,;), — This liquid also had been already ex- 
amined thoroughly in the old cell. When tried in the new 
cell it acts as a very good insulator (10), and gives excellent 
optical effects of the same kind as those of carbon disulphide 
(9). It requires no measurements, and very little observation, 
to show that this liquid is far inferior to the former in inten- 
sity and range of ett'ect. Benzol does give the extinction- 
bands clearly ; but they are never so fine as in CS2 ; and I 
think that I have never seen the bands clearly separated 
in benzol against a tension of more than two pounds in 
the fixed compensator. Still the electro-optic action is very 
fine, pure, and perfectly regular. The light restored from 
pure extinction by electric action in the cell is always extin- 
guished perfectly by compression of glass in a direction 
parallel to the lines of force, and always strengthened by tension 
in that direction. 

15. Tohiol (C7 H{<). — This liquid is very like benzol in its 
more patent physical properties ; like benzol also, it is a very 
good insulator, and gives a good optical etlect of the same 
kind as CSo under electric action. In the only two careful 
trials that I have given to this liquid, I found it particularly 
difficult to obtain a pui*e initial extinction ; and although this 
may have been caused by some unnoticed and accidental de- 
rangements of the solid parts of the apparatus, I suspect it 
was rather due to some faint specific action of the liquid. In 
other respects I could not observe any clear difference between 
toluol and benzol, the effects being equally regular and jnn-e, 
of exactly the same kind, and of much the same intensity and 
ranije. The lioht restored from ijood extinction in the polari- 
scope by electric action in the cell was always extinguished 
perfectly by horizontal compression or vertical tension of glass. 
The extinction-bands also were clearly developed in toluol, as 
in benzol, against a small tension in the fixed compensator. 

1(5. Xijlol (Cs H;io). — This liquid also is very like benzol in 
odour and appearance ; and it acts very similarly in the plate 
cell, both as an insulator and in electro-optic experiment. From 

Observations on various Liquids. 95 

the difficulty of cleaning it, I found it not a good liquid to 
AYork with. After many rinsings of the cell, the electrified 
balls were still connected Ly visible chains of particles ; and 
although the larger particles fell to the bottom of the cell in a 
little time, and the desired eliect came out very clearly, still 
the liquid was hardly ever purely transparent, but generally 
somewhat misty or faintly speckled. A\ ith this one drawback, 
xylol acted perfectly well in the electro-optic experiment (9). 
The optical effect was clearly stronger than that of benzol. 
The extinction-bands were well developed against a tension of 
two pounds. The light restored by electric action was always 
extinguished perfectly by horizontal compression of glass. 

17. Cumol (CgHio). — This compound is somewhat viscous, 
and not nearly so volatile as the preceding liquids. The only 
sample of it that I have worked with is of a faint yellowish 
colour, but purely transparent. When tested in the usual 
way, it acts as a good insulator (10). The optical effect of 
electric force is of the same kind in cumol as in the former 
liquids, and is equally i-egular and pure, being always neu- 
tralized perfectly by horizontal compression or vertical tension 
of glass. This liquid is likely to hold an important place in 
electro-optics : it is in all respects very easily managed as a 
dielectric ; and after CS2, which it follows indeed at a large 
interval, it gives an optical effect more intense and of longer 
range than any other liquid yet examined. Against a tension 
of four pounds in the fixed compensator, the extinction-bands 
are developed almost as finely in cumol as in CSg. 

When the electric action and the compensating strain are 
intense, the bands appear to assume a peculiar form in cumol. 
Eeturning to the experiment described in (12), where the two 
compensators were applied in combination with an intense 
electric action on CS2J it will be remembered that the effect 
of a strong compression of the hand compensator was to bring 
the bands in towards the axis of the field, where they finally 
coincided in one axal band. In cumol the effect takes a dif- 
ferent form. As the bands approach the axis, they become 
largely inclined to each other, convero;ino- from the outer 
parts of the surface of the niductric ball towards the intersec- 
tion of the axis of the field with the surface of the opposite 
ball. A contrary form of effect was observed in xylol, where 
the bands diverged from the axal part of the surface of the 
inductric ball toAvards the outer parts of the opposite ball. 
Other liquids gave traces of similar variations, but none so 
distinctly as the two that I have mentioned. Although I have 
not made a particular study of these phenomena, but have 
merely noticed them carefully in passing, I cannot believe 

96 Dr. J. Ken's Electro-optic 

them to have been accidental. They seem rather to indicate 
some specific differences between the several li(|uids, probably 
with reference to the distribution of electric force. 

18. Ci/mol (C10H14). — Colourless, transparent, and very 
distinguishable from benzol by its agreeable odour. It is an 
excellent insulator, and acts very similarly to benzol in electro- 
optic experiments, giving an optical effect of exactly the same 
kind, equally regular and pure, and of much the same inten- 
sity and range. The light restored by electric force in cymoi 
is always extinguished perfectly by compression of glass in a 
direction parallel to the lines of force. 

19. Terehene (Cjo Hje). — When the cell is charged with my 
only specimen of this liquid, the arrangements being other- 
wise as in the fundamental electro-optic experiment (8, 9), I 
find, contrary to expectation, that the light is rotated and sen- 
sibly dispersed in its passage through the cell ; still there is a 
good approximate initial extinction got between the red and 
blue. The liquid acts as a very good insulator, the sparks 
from prime conductor having apparently the same density and 
length when the connecting wires are in and out of place (10). 
In torebene, electric force evidently strengthens the light from 
approximate extinction in the ])olariscope ; and this effect is 
clearly weakened by horizontal compression of glass, and 
clearly strengthened by horizontal tension. The effect is not 
nearly so strong as in the members of the benzol series ; but 
it is certain, and certainly of the same kind. My former ob- 
servations on oil-of-turpentine with the old plate cell were at 
least as satisfactory as these on terebene. 

20. Amijlene ((J5 Hio)- — Colourless, transparent, and exces- 
sively volatile. Tested in the usual way, it acts as an excel- 
lent insulator ; long sparks from the prime conductor, or from 
connected ball of the cell, do not sensibly diminish in length 
or intensify when the earth-ball of the cell is touched by earth- 
wire or knuckle. In the electro-optic ex[)eriment, as for CS2 
(8, 9), amylene acts very finely, and in the same way as each 
of the preceding hydrocarbons, the eflect of electric action 
from extinction in the polariscope being always neutralized 
perfectly by horizontal compression of glass. Against a weight 
of one pound on the fixed compensator (11), electrization deve- 
lops the extinction-bands faintly, and moves them into the outer 
parts of the field ; but against a weight of two pounds, the 
effect of the strongest electric action attainable falls far short 
of extinction at the centre of the electric field. Amylene 
stands, therefore, between benzol and terebene. 

21. Valeric Acid (C5 Hjo O2).— Tested in the usual way, 
this liquid is not a good insulator. Sparks from the prime 

Observations on various Liquids. 97 

conductor are very much shortened and attenuated when the 
connecting-wires are placed ; and if the earth- wire be detached 
from the cell, the earth- ball of the cell (with shaft projecting 
a little way out of it) gives crackling discharge into the air 
whenever the machine is worked vigorously. In one careful 
trial of the electro-optic experiment, as for CS2, I obtained a 
continuous restoration from pure extinction in the polariscope. 
The effect was extremely faint, but perfectly regular, and was 
neutralized by horizontal compression of glass. In several 
Ibllowing trials I could not recover this phenomenon regu- 
larly. I have little doubt that the effect is real ; but it is one 
of the faintest that I have ever observed. 

22. Carbon Bichloride (Cg CI4). — Transparent, colourless, 
and a very good insulator. Under electric action, as in the 
preceding experiments (8, 9), carbon dichloride restores the 
hght from extinction in the polariscope. The effect is pure 
and regular, and is neutralized perfectly by horizontal com- 
pression of glass. The extinction-bands are well separated in 
this liquid against a weight of three pounds on the first com- 
pensator (11). Carbon dichloride stands, therefore, some- 
what above benzol. 

As this liquid was expensive, and as there was only a small 
quantity of it at hand, I had to be satisfied with charges that 
were not quite clean. As the experiment proceeded, the im- 
purities were apparently dissolved or absorbed in some way, 
and the plate improved remarkably in its optical action. 
Changes of the same kind were observed in some other liquids, 
but in a less degree. 

23. At this point I may mention some apparently trivial 
phenomena which I observed repeatedly in the course of the 
preceding experiments. On one occasion, when the cell was 
charged with CS2, the liquid had been allowed to evaporate 
until its free surface was nearly as far down as the tops of 
the balls. At the instant when the machine was set in mo- 
tion, the surface of the liquid was deformed ; over the centre 
of the field there was a hump raised which, by its form and 
position, reminded me of the arched extinction-bands (11). As 
long as the electric force was kept at a moderate and approxi- 
mately constant intensity, I could not detect any sure appear- 
ance of motion in the hump. Similar effects, though not so large, 
were obtained in benzol, also in carbon dichloride and other 
liquids. In cumol the hump was apparently as high as in CS2; 
but it was accompanied by vigorous movements in the liquid, 
apparent currents from ball to ball along and through the hump. 
In xylol the effects were very intense ; the movements were 
more violent than in cumol ; and when only a large bubble of 

98 Dr. J. Kerr's Electro-optic 

air was left in the top of the cell, it was drawn downwards by 
the conunotion of the strongly electrified liquid, and was 
broken up into many small bubbles, which danced rapidly 
throuoh the field, and prevented all regular optical effect. 

The imjirt%sion conveyed by the phenomenon in the case of 
CSo was that of a simply statical arrangement of the dielectric, 
a concatenation of electrically polarized particles of the liquid 
along the curved lines of force, the electric action being in- 
tense enough to overpower, so far, the gravitation of the par- 
ticles. In the case of cumol the impression was different ; 
the hump may have been produced, at least in part, by the 
strong convection-currents whieh always accompanied it. Not 
that there is any real inconsistency between these views ; for 
there may evidently be a regular tile-arrangement of particles, 
kept up continually, or, rather, incessantly renewed, along the 
curved lines of force, while there are gross currents of liquid 
passing incessantly between the balls. 

24. iV/V/'o/'^»ro/ (C^ II-, NOo), new electro-optic action. — This 
oily liquid, though yellowish in colour, is very purely trans- 
parent. Tested in the usual way, it acts as a good conductor 
(10). When the two connecting- Avires are in position, and 
the machine is worked vigorously, no sensible spark can be 
drawn from the ]n'ime conductor, no movement can be de- 
dected in the liquid, nor any trace of the hump (23). And, 
accordingly, in the clectro-ojitic experiment arranged and con- 
ducted as tor CSo (8), nitrobenzol gives no trace of optical 
effect, the extinction in the polariscope being as pure when 
the machine is worked at the hardest rate as when it is at rest. 
But it requires only a small change of the conditions to give 
a large effect. 

The first connecting-wire, that from prime conductor to cell, 
being kept always in ]:)osition, the earth-wire is detached from 
the second outer ball of the cell, and the observer at the polari- 
scope brings up his knuckle slowly towards the latter ball till 
a spark passes, the longer and denser the better. At the in- 
stant of the spark (that is, at the instant of abrupt discharge 
of the prime conductor through the liquid) there is a strong 
restoration from extinction in the polariscope, not a mere 
s])ark, nor a vague illumination, but a true restoration of the 
old object, bright and clear and well outlined, as in many of 
the former observations, though apparently instantaneous as 
the spark itself. 

As the knuckle is brought up slowly to contact with the 
ball, the restorations in the polariscope succeed each other 
more rapidly, and become individually fainter. Tlie light is 
by-and-by sustained continually, but never without a sen- 

Observations on various Liquids. 99 

sible flicker ; and it becomes fainter and fainter on the ayIioIo 
as the length of the spark diminishes, A httle befoi-e the 
spark vanishes, the restorations disappear to sense ; and from 
this point up to contact of ball and knuckle, and afterwards, 
the action of the machine is without sensible effect in the 
polariscope. I have made some additional observations on 
this form of effect; but, to prevent confusion, I reserve them 
for a little. 

25. Z?;-o»iio/«o/ (C7H7 Br). — In its electro-optic relations, 
this liquid resembles carbon disnlphide and benzol on the one 
hand, and nitrobenzol on the other, giving the two kinds of 
effect clearly, though not intensely. Tested in the usual way, 
it acts as an imperfect insulator. When the connecting-wires 
are in position, the sparks from the prime conductor are 
greatly attenuated, and are reduced in length from an inch or 
more to about an eighth of an inch. 

AVhen bronitoluol is examined electro-optically in the same 
way as CS2 (8), the electric action gives a continuous restora- 
tion from pure extinction in the polariscope. The effect is not 
strong ; but it is quite certain, and certainly of the same kind 
as in CS2, being neutralized perfectly by horizontal compres- 
sion of glass. And, again, when the discharging train from 
the prime conductor through cell to earth is interrupted at any. 
point by an air-interval, there is a good restoration in the po- 
lariscope at the instant of each spark, the effect being appa- 
rently of the same kind as that observed in nitrobenzol, 
though not nearly so strong. Bronitoluol is an inconvenient 
liquid to work with, partly from the very irritating, onion-like 
action of its vapour on the observer's eye, and partly from the 
difficulty of getting a clean charge — a difficulty that I have not 
once overcome perfectly. 

i'o. IVial of other Liquids for the Nitrobenzol Effect. — 
Carbon disulphide, carbon dichloride, terebene, and most of 
the other liquids already mentioned were all examined care- 
fully in the same way as nitrobenzol (24). The optical effects 
accompanying discharge were either insensible, or of the kind 
noted in the two following cases. 

Amyiene. — The spark's obtained from the earth-ball were 
very short and attenuated, and were accompanied by distinct 
restorations in the polariscope. The restorations were far from 
instantaneous, each of them rising sensibly to a maximum in- 
tensity, and then sensibly falling. The effect improved in 
strength as the knuckle approached the ball till the leno-th of 
the spark reached zero ; and then the effect was to sense con- 
tinuous, and certainly at its greatest intensity. 

Benzol. — The sparks from earth-knob to knuckle were very 

100 Dr. J. Kerr's Electro-optic 

short, not more than an eighth of an inch, when those from tlie 
prime conductor were about an inch. The sparks were ac- 
companied by an abnost continuous effect in the j)olari.scope, 
wliieh iin[)roved as tbe knuckle approached the ball. At con- 
tact of ball and knuckle tlie optical etfect was contiimous, and 
certainly at its greatest intensity. In these two liquids, and 
in all the other insulators that gave any distinct etfect, the 
phenomenon was apparently of the same kind through its 
whole progress, and very unlike that obtained from nitro- 

27. Stannic Chloride (SnClt). — I was sorry to find, on trial, 
that my method is quite inapplicable in the case of this in- 
teresting compound, one of the best insulators known among 
liquids. Still the trial ought to be described, as it gave me a 
good glimpse of what I believe to be a new fact. The liquid was 
let into the cell as rapitliy as possible, through filtering-paper 
and funnel. During this brief exposure to the air, which 
was unfortunately rather moist at the time, the liquid gave 
otf a dense white cloud of suffocating fumes. The liquid, as 
it rose in the cell, was fairly transparent; but above it there 
lay a deep shell of dense white froth. The charging of the 
cell was completed in several seconds. The most of the froth 
had run over the mouth of the vertical boring, and was rapidly 
wiped away ; but some of it had evidently dissolved in the 
liquid, giving it a uniformly milky or misty aj)pearance, 
deadening the transparency without seriously impairing it. 
As all the pieces had been already put in final position for the 
electro-optic experiment (8, 9), the second Nicol was now 
turned at once to good extinction, and the machine was set in 
motion. At the first turn of the i)late there was a vivid resto- 
ration in the polariscope, stronger a great deal (such at least 
was my impression at the time) than any thing of the kind 
that I had yet seen, even in the case of CS2. The hand com- 
pensator was immediately applied in the usual way (4), but 
without a trace of the ordinary effect : the light restored by 
electric force was not sensibly weakened either by horizontal 
tension or by horizontal compression. This result was so un- 
expected, and, indeed, so extraordinary, that I had to spend a 
little time in making sure there was no mistake. Trying 
other means, I soon found that the effect of electric force was 
neutralized, either perfectly or very nearly, by a definite ro- 
tation of the second Nicol through a small angle ; and up to 
this point I am veiy confident of the facts. 

Bv this time the liquid had evidently deteriorated, not as an 
insulator, but as an optical medium ; it had become in appear- 
ance faintly discontinuous, partly speckled and partly reticu- 

Observations on various Liqtiids. 101 

lated, showing that the fine deposit was in course of agglo- 
meration. Among other trials now made, the first Kicol was 
turned throuorh a right angle, the second Nicol was turned 
into the position of best attainable extmction, and the electro- 
optic observation was repeated. Nothing like a good extinc- 
tion was obtained in this case ; but the effect of electric action 
was still considerable ; and it was evidently and considerably 
weakened by a rotation of the second Nicol through a small 
angle, the direction of this rotation being contrary to that 
obtained in the first case. Several other charges of the cell 
were tried from the same bottle ; but they were all speckled 
or gritty from the outset, and gave no distinct effect. As far 
as I can judge from memory and from imperfect notes taken 
at the time, I think that the optical action of electric force 
thus manifested in stannic chloride is to diminish the acute 
angle between the plane of polarization and the lines of force. 
Such is the best account that I can give of an observation 
which was unavoidably hurried, confused, and unsatisfactory. 
The experiment is not one that I should like to repeat in the 
same form ; it puts the instruments quite out of working order, 
and tends also to damage them permanently. 

28. Other Liquids tried, but tcitliont effect. — Of these I may 
mention particularly chloride of sulphur, pentachloride of anti- 
mony, trichloride of phosphorus, tetrachloride of carbon, sul- 
phide of allyl. These all acted as conductors (10), and gave no 
sensible effect in the polariscope under electric force (8). I 
should except sulphide of allyl, which gave good, though very 
faint, traces of the nitrobenzol effect (24). I have little doubt 
that the failure of most of the perchlorides was due to traces of 
water, for which these compounds have an intense attraction. 

All the liquids mentioned up to this point were obtained as 
pure chemicals from the establishment of Burbidge and 

Organic Liquids. 

29. Young''s Paraffin Oil. — Specific gravity '814, a trade 
sample of an illuminant, one of the lightest made, clear as 
water, and an excellent insulator. In the electro-optic expe- 
riment, as for CS2, this liquid gives a very fine, but faint 
effect : the light is well restored by electric force from pure 
extinction ; and the effect is neutralized perfectly by horizontal 
compression of glass. In intensity and range of effect, this 
paraffin stands between amylene and terebene, but a good deal 
nearer the latter. An illuminating paraffin was tried long 
ago in the old plate cell, and with like effects, though much 

Phil. Mag. S. 5. Vol. 8. No. 47. Aug. 1879. I 

102 Prof. II. A. Kowland oi a new Tlieory 

30. Yoiivg's Parafin Oil, specific gravity *800, a trade 
sample of one of the heaviest lubricants made ; brownish in 
colour, fluorescent, transparent, and a very good insulator. 
In electro-optic experiments tho action of this paraitin is 
similar to that of tho preceding, equally regular and pure, 
but remarkably stronger. The extinction-bands arc as fine 
in this liquid as in cumol, if not finer. Against a weight 
of 4 pounds on the fixed compensator the bands are easily 
moved out beyond the balls ; but against a weight of 7 pounds 
the axal band is barely, if so much as, divided. There is no 
other licpiid that I have examined, except CSg, which is clearly 
superior to this heavy paratfin in strength and range of electro- 
optic action. I am not sure whether cumol should be placed 
above or below it. 

Gl{u«gow, July 1, 1879. 

[To be continued.] " 

XII. On Professors Ayrton and Perry's neio Theory of the 
Earth''s Magnetism, with a Note on a nexo Theory of the 
Aurora. By H. A. Eowland, Professor of Physics in the 
Johns Hopkins University* . 

SOIME years ago, while in Berlin, I proved by direct expe- 
riment that electric convection produced magnetic action ; 
and I then suggested to Professor Helmholtz that a theory of 
the earth^s magnetism might be based upon the experiment. 
But upon calculating the potential of the earth required to 
produce the efiect, 1 found that it was entirely too great to 
exist without producing violent perturbations in the planetary 
movements, and other violent actions. 

I have lately read Professor Ayrton and Perry's publication 
of the same theory ; and as they seem to have arrived at a 
result for the potential much less than I did, I have thought 
it worth while to publish my reasons for the rejection of the 

The first objection to the theoiy that struck me was, that 
not only the relative motion but also the absolute motion 
through space of the earth around the sun might also produce 
action. And to this end I instituted an experiment as soon as 
I came home from Berlin. 

I made a condenser of two parallel plates with a magnetic 
needle enclosed in a minute metal box between them ; for I 
reasoned that, when the plates were charged and were moved 
forward by the motion of the earth around the sun, they would 
then act in opposite diiections on the enclosed needle, and so 
*■ (Joinnumicnted hy the Physical Society, having been read June 20th. 

of the Earth! s Magnetism. 103 

cause a deflection when the electrification of the condenser 
■was reversed. On trving the experiment in the most careful 
manner, there was not the slightest trace of action after all 
sources of error had been eliminated. 

But the experiment did not satisfy me, as I saw there was 
some electricity on the metal case surrounding the needle. 
And so I attacked the problem analytically, and arrived at the 
curious result that if an electrified system moves forward with- 
out rotation through space, the magnetic force at any point is 
dependent on the electrical force at that same point — or, in 
other words, that all the equipotential surfaces have the same 
magnetic action. Hence, when we shield a needle from elec- 
trostatic action, we also shield it from magnetic action. 

This theorem only applies to irrotational motion, and 
assumes that the elementary law for the magnetic action of 
electric convection is the same as the most simjyie elementary 
law for closed circuits. Hence we see that, provided the earth 
were unifonnly electrified on the exterior of the atmosphere, 
there would be no magnetic action on the earth's surface due 
to mere motion of translation through space. 

In calculating the magnetic action due to the rotation, I have 
taken the most favourable case, and so have assumed the earth 
to be a sphere of magnetic material of great permeability, fi. 
It does not seem probable that it would make much difl^erence 
whether the inside sphere rotated or was stationary ; or at 
least the magnetic action would be greatest in the latter case ; 
and hence by considering it stationary we should get the 
superior limit to the amount of magnetism. 

Let a be the radius of the sphere moving with angular velo- 
city ic, and let cr be its surfiice-density in electrostatic measure, 
and n the ratio of the electromagnetic to the electrostatic unit 
of electricity. Then the current-function will be 

<}> = l^ca''Y 

sm$dd=: ica^ cos d. 

Hence (Maxwell's 'Treatise,^ § 672) the magnetic potential 
inside the sphere is 

\l— ^ — war cos t/, 

and outside the sphere 

^, 4 a ^cos^ 
ii = Kir - ica — rj— • 
6 n r 

The magnetic force in the interior of the sphere is thus 


-p 8 cr 
r = o TT - iL-a. 

104 Proi. H. A. Rowland on a new Tlieory 

or the field is uniform. If the electric potential of the sphere 
on the electrostatic system is V, wc may Avrite 

6 n ' 

which is independent of the dimensions of the sphere. 

In this uniform field in the interior of the sphere, let a 
smaller sphere of radius a' be situated ; the potential of its 
induced mairnetization will be 

^ /a + 2 r^ 

Hence the expression for the potential for the space between 
the two spheres Avill be 

TT 2 «' ^ r /, At— 1 ,,cos^) 

U=5-Y-J -rcos<9+^^^a'3— ^ >; 

and outside the electrified sphere it will be 

jLt— l\cos^ 

Let us now take the most favourable case for the production 
of magnetism that we can conceivej making a'=-a and /u, = co ; 
we then have 

11 r 


which is the potential of an elementary magnet of magnetic 


But Gauss* has estimated the magnetic moment of the earth to 

3-3092 a^ 

on the millimetre mg. second system. Hence we have 

Y= 3-3092- 

for the potential in electrostatic units on the mm. mg. second 
system. In electromagnetic units it is thus 

Yi= 3-3092 -; 


and hence in volts it is this quantity divided by 10^^ 
* Taylor's Sclent. Mem. vol. ii. p. 225. 

of the Earth's Magnetism. 105 

As the earth makes one revolution in 23'^ 56' A!', or in 
86164 seconds, we have 



?« = 299,000,000,000* millims. per second. 

Hence the earth must be electrified to a potential of about 

41 X 10^^ voltsf 
in order, under the most favourable circumstances, to account 
for the earth's magnetism. This would be sufficient to pro- 
duce a spark in atmosi^heric air of ordinary density of about 

6,000,000 miles ! 
Professors Ayrton and Perry have only found the potential 
10^ volts, or 400,000,000 times less than I find it. 

It was this large quantity which caused me to reject the 
theory: for I saw what an immense effect it would have in 
planetary perturbations ; and I even imagined to myself the 
atmosphere flying away, and the lighter bodies on the earth 
carried away into space by the repulsion. And, doubtless, had 
not Professors Ayrton and Perry made some mistake in their 
calculation by which the force was diminished 16 x 10"^^ times, 
they would have feared like results. 

For according to Thomson's formula, the force would be 
equal to a pressure outwards of 


■>'= Q 2' 

which amounts to no less than 

1,800,000 grms. 
per square centimetre ! or 10,000 kil. per square inch ! 
Such an electrostatic force as this would undoubtedly tear the 
earth to pieces, and distribute its fragments to the uttermost 
parts of the universe. If the moon were electrified to a like 

* From a prelimiuaiy calculation of a new determination made with 
the greatest care, and having a probable error of 1 in loOO. 

t That this is not too great may be estimated fi-om my Berlin experi- 
ment, where a disk moving 5,000,000 times as fast as the earth with a 
potential of 10,000 volts, produced a magnetic force of j^ ^jj-q of the earth's 

5,000,000 X 10,000 X 50,000 = 2,500,000,000,000,000, 

which is of the same order of magTiitude as the quantity calculated, 
namely 01 X 10^\ It can be seen that this reasoning is correct,^ because 
the foi-mulfe show that two spheres of unequal size, rotating with equal 
angular velocity and charged to the same potential, produce the same mag- 
netic force at similar points in the two systems. 

106 On a new Theory of the Aurora. 

potential, the force of repulsion would be greater than the 
gravitation attraction to the earth, and it would tlj off through 

For those reasons I rejected the theory, and now believe 
that the magnetism of the earth still remains, as before, one 
of the great mysteries of the miiverse, toward the solution of 
which we have not yet made the most distant approach. 

In connexion with the theory of the earth's magnetism, I 
had also framed a theory of the Aurora which may still hold. 
It is that the earth is electritied, and naturally that the elec- 
tricity resides for the most part on the exterior of the atmo- 
sphere — and that the air-currents thus carry the electricity 
toward the poles, where the air descending leaves it — and 
that the condensation so produced is finally relieved by dis- 

The total effect would thus be to cause a difference 
of potential between the earth and the upper regions of the 
air both at the poles and the equator. At the poles the dis- 
charge of the aurora takes place in the dry atmosphere. At 
the equator the electrostatic attraction of the earth for the 
upper atmospheric layers causes the atmosphere to be in un- 
stable equilibrium. At some spot of least resistance the upper 
atmosphere rushes toward the earth, moisture is condensed, 
and a conductor thus formed on which electricity can collect; 
and so the whole forms a conducting system by which the 
electric potential of the upper air and the earth become more 
nearly equal. This is the phenomenon known as the thunder- 

Heiice, Avere the earth electrified, the electricity would be 
carried to the higher latitudes by convection. Mould there dis- 
charge to the earth as an aurora, and passing back to the 
equator would get to the upper regions as a lightning dis- 
charge, once more to go on its unending cycle. I leave the 
details of this theory to the future. 

Baltimore, May 30, 1879. 

Appendi.T. — Since writing the above. Professors Ayrton and 
Perry's paper has appeared in full ; and I am thus able to point 
out their error more exactly. Their formula at the foot of 
page 406 is almost the same as mine ; but on page 407, in the 
fourth equation, the exponent of n should be +i instead of 
— •^, which increases their result by about 600,000,000, and 
makes it practically the same as my own. 

Eotterdam, July l;Uh. 

[ 107 ] 

XIII. Carbon and Carho-Hydrogen, Spec troscoped and Spe- 
trometed in 1879. By PiAZZi Smyth, Astronomer Royal 
for Scotland*. 

a"lHE recent spectroscopic observations of Brorsen's Comet 
havinor brought aorain into view the strange contradiction 
■which still exists, between chemists on one side, and most spec- 
troscopists on the other, touching the temperature at which 
pure carbon vapour can possibly be volatilized, the present 
may be an appropriate occasion for describing a few recent 
steps in the inquiry, especially as they may haply be found 
to shed some new light on the difficulty undoubtedly inherent 
in the case. 

On the one hand, the chemists are represented as uniformly 
agreed that pure carbon is, to all their methods of trial by 
furnace- heat, next to impossible to drive olF into vapour. And, 
on the other hand, not only some, but I am told that almost 
all the great spectroscopists of the day have found, according 
to their examinations of precision, that the vapour of carbon 
is given oft' freely in the moderate heat of every kind of little 
candle- or lamp-flame (I) — this being evidenced to them by a 
spectrum Avhich they declare is that of pure carbon, though 
some two or three persons in, by this time perhaps rather to 
be considered out of, the community, persist in holding it to 
be the spectrum of only the coiiipound gas " carbo-hydrogen." 

This last spectrum, carefully described by Professor Swan, 
in Edinburgh in 185G, as being that of '' carbo-hj-drogen," 
was nine years later pronounced by Dr. Attfield in London 
to belong to pure " carbon," and has now, after many inter- 
vening researches by other men, very recently been still more 
minutely examined by me in its most standard form of a coal- 
gas and common-air blowpipe-flame, viewed end on. This 
mode of observing it is of extraordinary advantage for seeing 
the fainter lines, and allowing higher dispersive power of prisms 
to be employed. But it did not actually reverse any thing of 
moment in Professor Swan's primary description. It only 
extended and added details — utilizing even most of the mere 
haze which earlier observers had noticed hanging about the 
bands of graduated lines, by resolving it into little attendant 
lines or linelets. Hence there is no dispute about all the chief 
physiognomy of this spectrum ; and the only difterence of 
opinion is, the rather extreme case in physics, as to whether it 
belongs to the easily volatile compound " carbo-hydrogen, '' or 
the most refractory and involatile element " carbon." 

* Communicated bv the Author. 

108 Mr. Piazzi Sin}'th on Carbon and Carho-IIydrogen, 

Tlio startlin;^ deduction that tlie sitcctruin bolonrrs to carhon 
is claimed to have been ])roved by Dr. Attfield, Dr. ^Marshall 
Watts, and otlier most able men, from their havin;^ found one 
and the same spectrum in all compounds of carbon — i. e. not 
only in carbo-hydro^rens, but in carbo-oxyorens and cjvrbo- 
nitrogens of several kinds, first in blowpipe flames, and then 
in gases illumined by the electric spark, both at ordinary at- 
mospheric pressure and in vacuum-tab(?s. 

Of these several methods I have only been able to test the 
last through many varieties of carbon, and other, compounds. 
But that method I have not only had superior vision of by 
means of my recently constructed end-on tubes (made for me 
by M. Salleron, 24 Rue Pavee an Marais, Paris), but have 
examined its manifestations under more powerful dispersion 
than most of my predecessors. And with what result ? "With 
the astonishment of finding that after all, while something 
certainly visible is undoubtedly common to all the tubes, there 
is another thing visible, in some of them even to greater 
brightness, and is so seen in carbo-bydrogen tubes only. 

First, let us bo quite clear on what that previous something 
was, which was common to all the tubes. 

It is a spectrum somewhat like the coal-gas and air blow- 
pipe-flame spectrum, having, besides other features, five co- 
loured bands — red, citron, green, blue, and violet — -and each 
band capable of breaking up into thin compound lines under 
high dispersion. But no band of one of these spectra begins 
exactly in the same place as any band in the other ; nor are 
its minuter constructional lines in the least degree similar. 
Dr. Watts, moreover, does recognize this vacuum-tube spec- 
trum as being ditterent from the coal-gas blowj)ipe-flame's 
spectrum, and calls it therefore " the second spectrum of car- 
bon." A carbon-spectrum, too, I will not deny it may be; for 
the temperature of the disruptive induction-spark under which 
it is produced, may be quite enough to dissociate even that 
element from its compounds and keep its vapour incandescent. 
But let us examine the said possible carbon-spectrum from 
tube to tube, and note the variations. 

Now here our first entry must be, that this alleged tube 
carbon-spectrum appears in evern vacuum-tube I possess, whe- 
ther j)ur])orting to contain a compound of carbon or not ; but 
it varies in brightness. Hence it appears moderatelij only in 
tubes of 

Air, Ozone, 

Nitrogen, Hydrogen, and 

Oxygen, Nitrous Oxide ; 

Spectroscoped and Spectrometed fn 1879. 109 

but it manifests itself excessively in tubes of 

Cyanogen (carbo-nitrogen). 

Carbonic acid and carbonic oxide (carbo-oxygen). 

Also with extreme bricrhtness in tubes of 


defiant gas, and 

Marsh-gas (all carbo-hydrogens). 

Whence Ave may safely conclude that the spectrum appears 
in the six first tubes solely as an impurity of some kind ; and 
the abundant carbonate of soda used by the glass-makers for 
such tube-glass may be its origin. Hence it is the excess of 
intensity between those six first, and the six last, tubes which 
"vve are to look to alone as the possible carbon-spectrum of the 
carbonic compound gas proper to the tube. Pure hydrogen- 
lines (probably derived from infinitesimal traces of moisture) 
also appear in every one of the 12 tubes, except the cjMuogen ; 
and there they are strikingly absent. 

Confining our attention now, for the sake of greater accu- 
racy with economy of time and labour, Avhen using a high dis- 
persion (33° from A to H, and mag. power = 10), to the green- 
band region alone of the tube-carbon-spectrum, that band 
does seem to be, throughout all the tubes, identical — even mi- 
croscopically identical in every one of its earlier and brighter 
minute constructional lines ; and it varies only, at least in that 
earlier part, in the mere matter of general development or 
strength and intensity from tube to tube. 

Those constructional lines of the vacuum-tubes' green band 
are closest and brightest on that side of it which is toward the 
direction of least refrangibility (/. e. towards the red), begin- 
ning at Wave-Xumber place 48,861; and they include, after 
a few of their lines towards the direction of greater refrangi- 
bility (i. e. towards the violet), or at Wave-Number place 
48,969, a peculiar crossing over each other of two sets of lines. 
That spot, marked extra brightly by one line just overlapping 
another, is very easily identifiable by the eye, at least in my 
spectroscope, even when the spectrum is but faintly deve- 
loped; and it forms a convenient step for an observer, when 
first roughly journeying optically from the strong and sharp 
beginning or least refrangible and the red-icard edge of the 
said vacuum-tube carbon's green band, onwards to its more 
refrangible and fainter, and violet-ward regions, in search of 
any thing possibly abnormal in any one tube or another. 

Instituting this quest, if we examine all our first mentioned 

110 Mr. Vnu/A Smyth on Carbon and Carbo-IIydrogen, 

six tubes, viz. air, nitro<Ten, oxygen, ozone, Lydrogen, and ni- 
trons oxide, we shall hnd little or nothing unusual therein, 
but only see the fainter and still more faint ])rolongations of 
the green band going off in that violet-ward direction. 

In cyanogen, carbonic acid, and carbonic-oxide tubes, how- 
ever, there is something suspicious that in one certain S})ot in 
each of them — as far beyond, or violet-ward, of the crossing- 
j)lace of lines as that is from the strong red-ward beginning 
of the tube-carbon's green band, there is a sort of smear, or 
half rubbed-out line — in fact, looking more like an impurity 
trace than a proper constituent of the chemical compound 
under trial. 

But in the alcohol and olefiant gas-tubes (and even in the 
marsh-gas as well, though not so strongly) that sort of chalked 
place is occupied by a l)rilliant colossal bright line, so glaring 
that it almost extinguishes by its su])erior h'ght the fine thin 
lines of the tube-carbon band in the neighbourhood. And 
twice as far onward, still in the direction of increased refran- 
gibility (or violet-ward), there is another similar and, though 
less bright line, still a very notable one to meet with in that 
part of the spectrum. 

Now what are these two bright lines which appear so con- 
spicuously in all three of our carbo-hydrogen tubes, but in no 
other compounds of carbon, though we have been hitherto 
told by several famous observers that there is no difference 
amongst any of them ? 

By most careful reference from the electrically illuminated 
vacuum-tubes to the bloAvpipe flame, I ascertained that the 
strangers were the first and second lines of the (rreen band of 
the coal-gas and air blowpipe-flame. Proving that even at 
induction-spark temperature that remarkable and humanly 
most useful compound, carbo-hydrogen, excitable at first by 
merely the flame of the smallest candle, is not yet comj)letely 
dissociated into its elements. 

Perhaps more powerful sparks than the one-inch ones em- 
ployed by me might dissociate the whole of the carbo-hydro- 
gen in the tube ; and then we should have only the tube-carbon 
bands and hydrogen- lines with some possibility of impurities, 
while the })Oor old blowpipe-flame's spectrum would be no- 
where. And whether some immensely and still more pow- 
erful and also jar-condensed electric sparks may not be able 
vet further even to break down the already described tube- 
carbon spectrum with its bands (composed really of innume- 
rable and closely-])acked, but very thin, sharp lines and line- 
lets), and produce a second and linear spectrum of carbon 
composed probably of a few only, and far brighter and difte- 

Spedroscoped and Spectrometed in 1879. Ill 

rently placed lines, may well admit of hope, and persuade to 
the trial those who have the requisite apparatus. So that they 
may thus yet be able to do for carbon, what the late lamented 
Professor Pliicker asserts he did for nitrogen, when by dint 
of 6-inch sparks and Leydcn-jar condensers he changed the 
form of nitrogen's spectrum from its earlier, or cooler, con- 
dition of numerous bands composed of innumerable ranks of 
microscoj)ic linelets, into its now well-known (and first by 

M. Angstrom discovered) linear character of a few much 
brighter lines only*. 


Premising then once more, that though by means of the 
surpassing brilliancy of end-on vacuum-tubes and large dis- 
persion, I may be able to give many observed and sharp lines 
in the green band of tube-cai-bon (more perhaps than have 
ever been previously registered for it within the same narrow 
limits of spectrum place), they form part of only the possible 
ta?ifZ-spectrum of carbon, our vacuum-tube-carbon, after all — 
I now propose to append a table of measures to show exactly 
where the first and second big lines, as well as the numerous 
little linelets of the compound carbo-hydrogen's green band 
so signally come in as an addition, when a carbo-hvdroffen, 
and not a carbo-oxygen or carbo-nitrogen, tube is employed. 

Now the first W.N. column in our duplex Table shows the 
tube-carbon spectrum's green band, as it was seen in a car- 
honic-oxide (carbo-oxygen) vacuum-tube. And if we simply 
add to that spectrum what is given in the second W.N. column, 
or the blowpipe-flame spectrum's green band, we shall have 
the tube-carbon green band very nearly as it presents itself in 
a carho-hydrogen vacuum-tube. Very nearly, I say only, not 
quite ; for the actual spectrum observed in the said tube gives the 
ribbing of the linelets of carbo-hydrogen (between say 49,400 
and 49,800 W.X. place) clearer and on a darker background 
than what would result by artificially combining or superim- 
posing on each other the separately observed carbonic-oxide 
tube-carbon spectrum and the blowpipe-flame's carbo-hydro- 
gen spectrum. 

Then in that case carbonic- oxide has added certain weak 
hazy bands to the fainter and more violet-ward parts of the 

* While copying out this paper for the press I have heard from Prof. 
Alex. S. Herschel of a memoir by M. Thalen, the admirable spectrosco- 
pist of Upsala, -who seems to have already obtained, in concert then 

■with his now deceased friend !M. Angstrom, just such a linear spectrum of 
carbon. But exactly how, I have yet to learn, as the memoir has not yet 
arrived in Edinburgrh. 

112 Mr. Piazzi Smyth 07i Carbon and Carbo-IIi/drogen, 

pure tube-carbon-spectrum, just as carbo-hydrogen adds its 
brilliant lines and many linelets when it has the opportunity 
in one of its own tul)es. 

Exactly so ! i3ut in such case what does a carbo-nitrogen 
tube do ? 

On examining carefully I found that it added a feature ex- 
cessively faint, but perfectly peculiar to itself, and somewhat 
reminding one, though at extreme distance, of the bands of 
nitrogen ; for there were many rather regular haze-bantls, be- 
ginning sharply, sometimes with an actual line, on the side of 
least refrangibility. One such line I would particularly call 
attention to, of intensity 1*0, and at W.N. place 4i),543; for 
while it appeared so very clearly in a cyanogen-tube, I con- 
vinced myself again and again that it did not exist (unless 
homa*opathically asan impurity trace) in either carbo-hydrogeu 
or carbo-oxygen tubes. 

Here, then, we have arrived at a most notable stage in our 
general inquiry ; for by pushing the examination to further 
exactitude than has been usual, we have found, in direct oppo- 
sition to general belief hithei'to : — 

1st. That each oi" the three varieties of compound carbon 
gases, viz. carbo-hydrogen, carbo-oxygen, and carl)o-nitro- 
gon, gives the later, or more violet-ward, details of the tube- 
carbon's band-spectrum (under 1 inch induction-spark) diti'e- 
rently from the other. 

2nd. That the feature Avhich is thus peculiar in a carbo- 
hydrogen tube is undoubtedly the well-known and most bril- 
liant coal-gas and air blowpipe-tlame's carbo-hydrogen spec- 

3rd. Whence we conclude that the pale and weak residual 
feature which is peculiar to a carbo-oxygen tube must there- 
fore be the carbo-oxygen flame's spectrum in open air, and 
the feature peculiar to the carbo-nitrogen tube the carbo- 
nitrogen flame's spectrum similarly. 

4th. In which case, attending to what has been already 
remarked as to respective intensity and faintness of lines and 
haze in the observations, we may see that whatever carbo- 
hydrogen succeeds in introducing into one of its own tube- 
spectra isjust as remarkable for enormous overpowering force 
as what either the carbo-oxygen or carbo-nitrogen introduces 
is for ultra weakness. 

5th. Wherefore in flame-spectroscojiy, when burning carbo- 
hydrogen gas in a blowpipe, the carbo-oxygen and carbo- 
nitrogen impurities, even though present to a large percentage, 
cannot make their faint spectra appear in the presence, or to 
the prejudice, of the carbo-hydrogen ; while, again, if we take 

Spectroscoped and Spectrometed in 1879. 


primarily either of those (carbo-oxygen or carbo-nitrogen) 
compound gases and burn it in a blowpipe, then if the smallest 
trace of carbo-hydrogen, merely as an unayoidable impurity, 
be present, its spectrum will oyerpower that of the gas proper 
to the occasion, and may lead to some unfortunate genera- 

Postscript. — By the kindness of Prof, Alexander S. Her- 
schel I am now enabled to add the yeritable /if n^a?* spectrum of 
carbon as giyen by M. Thalen in Xoya Acta R. S. Sc. Upsala, 
Series iii., yol. ix. 1875, in both description, number, and 
graphical representation. 

It was obtained apparently by the disruptiye discharge of 
electricity of high tension and in large quantity (" decharge 
disruptiye d'un gi'and condensateur, bobine de RuhmkorfF 
grande dimension "), and records only eleyen lines in the whole 
spectrum ; but each of them is remarkable for strength and 
clearness, thus : — 




Yellow and 
Citron . . 





Grand double f 1st component 

line \2ad „ 

Single line 

fist component 
2nd „ 

Single line 

f Ist component 
Triple group... \ 2nd „ 

I 3rd 
Yery broad line 





Place per 
Brit. inch. 



Hence these are the lines which should be alluded to, with 
all the responsibility of their fearfully high temperature of 
production, whenever any one in future speaks of " carbon 

Indeed M. Thalen goes further, and declares that this is 
the one, and only, spectrum that carbon alone is capable of 
under any circumstances whateyer ! But as he allows that 
his demonstration of that point is not yet quite complete, and 
as he does not seem to haye discoyered the peculiar micro- 
scopic arrangement of the linelets in what I haye ventured to 
call the vacuum- tube carbon's hand, or lower-temperature, 
spectrum, I conclude here with giving my recent measures 
of them in their green band ; thus — 

114 Mr. Piazzi Smyth on Carbon and Carho-IIydrogen, 





^— ^ 





<; CJ 





1— I 


















































P O 

.5 ^ 


c o c 

t. ■— -" 

-=> S^ ° 

a '' >< J^ 

en 1 

O o p o 


< ~ i-- 

a '3 - C cs 

hH cug 

o "ti '' 

of Carb 


!^ o 

•:7 oj C (c ;: ^^^'— • ^ u ^ <*-> & 

2 © p-l 

? t S ^ ^-2 c -^ o cc: ^ o o 


■5 ? 


s i 3 

■2 s 

The Gree 
least re 
and air 




:: ?oooaJS e-TS o*^ 


B8 of 


COCCO t- t-l>-t- O OOi^SiO 

^ V a 

■ f=^ - :u «• 

WW 5 i- 

^-it-'M 05-^?00 OQOeooo 
O t= --r t:- l- CO <r. O -H ^ d c^ 

o i 3 p 

>« u -^.s 


X' X X X) X X 00 CJ ci c; C5 ci 

x-xxao" QD'Qd'x"oo" x'od"qeoq 

2 a § S* 

■*■*■*!■*' Tfi Tf tt ■^ •* Tr ■^ Tji 

s-r-^ ^ 

1 . JL • 

— •- o i« 

5 X t-. 

IB g 3 fl 

all in 



' ' I*^ 

-on Car 
n a SIM 
s, each 

iC lO ir; iM ~; ut is ui »q 

;-,^^^ o-^-^-^ o6<i>i> 


-S 3 2 ® 

'= ^ 7. Z 

§ C <o»--^ 



n in a 
ry of 


5 ^ 

-^'H'? -S 

The Green Band of 
ward side: as see 
mined by 1-inch 
bichromate batte 



lll J 

a in -^ 


c t 











Spectvoscoped and Spcctrometed in 1879. 


c c 


a ^B 












^ ^ 






. ^ 








JO a SO ' .-^TS tj o o 

a c g - p 

i 3 2^3 

□"S 50 ?! O — 

cS OJ oj -^^ • — 

_^ o "^ f* 

-= eS iT ir. ^ 

K^ © o .s 

•4- t>.5 '^ <B j; 

S . « o - 

"^-G a ^ 

^ ~ a o 

IE o .0 a .»; a ^ 'o 

■" O cu « r^ 

«" — <B a a <u id s'-S 

3 a ^1 
_ oi CO _a g . 

; t, " o a ;£ 
;c2 Otis 60 ? 

a 'r ,aj '^ 

o ;i3 
^ ^ 5 5a ■„ 
■?: o a ^ a^ 
a •" cs -w -3 
a-5 d o d 
3 &: cr a a 

5 fee 

O C) 

5:3 S 
- ^-^ 
O ° 2 

!?r d 

Z [5 C3 

i S.2 

t-O O (M 

o t— 00 10 

O O M O 


C5 05 



00 a> 



coco o CO 
cjo' 00" cT ci" 

10 'M 
CO Tf 

(M C5 00 O CO 

00 00 C^ CO 

00 coco coco coco coco 

1 IG Mr. Plazzi Smyth on Carbon and Carho-Hydrogen, 

M 2 
•r; bD 


a « 




- *> rH 

fl 03 W 


S .. a 

S ?^ ^ 
^^ ^^ 

°l i 

■-C ^ 05 

S CD g 

a in > 
ID u-, ^ 
O <1> O 

J J '3 

• i-( 03 


l>^ C-1 IM CC CO -* 

C ■* CO C5 -^i 

T— -M -M Tl-?!^ 

^ "^ -^ Tf" "^ 

<D o t. Oi 

C - , -r J 


rs =s 

I— t^ t^ i~ i~ r^ 

6 c c c 6 ±> 

t- 1^ 1^ t^ t^ 


0) g 

^ a 

^ CI CO -t lO o 
^^ ,^, ^ 

m *i oi " 03 a 
-^ <c ^ o »^ w 
JJ tc ci o -^ -s 

° m b-, '^ ^ 3 



J; S o o o o 2 


13 S -^ O 

Oj — ' S 

i- ri: • — m 

t- -^ *> 

O <!' rt -3 

S ^-^ -9 

I a § 2 

O 3^ 3 

t. ^ g O' 

O r- 



n3 tn c =S 

-S " 

C a •- -Ja 






^ ^ a:s 



■ ^ 



S- o 


Cl o o cq 

1— < — 1 

(M CI 


Tj- ^ Tt( Tfl -* 


C: OS 

o ic IS o 00 00 

6 6 666 6 6 

,'5 '^-^-=1 

' 5 tD- 

ci .a 

x: '-' 



Spectroscoped and Spectrometed in 1879. 


O l^ --T 1> i-- n t- -.T 

O X 3 ■M O 


r-( -M- 

■^ C5 



5 lO 1> lO 

^^ r— ( »- 


T— t F 

—. T— I 


»o o 



-^ -~ -t. 

■-< t- 

"M ~ O -M 




l^ -^i 

CI O ~ 




cq ct 


t- t^ 

X r: — — 1 


It -T 


iO t^ 

c; -M '^^ o 


Cl 0-} 

■M ri 

5^1 ■>! T-1 

•M Tl 


^ -f 



c; — . 



^rt< -f 


-r -r 

-J. -J, -4, ^ 



— -Tl 


^ rf 


r-t- i~ 


t--. t- t- t>- t- 

t>- 1~ t- t^ l>- 

t- t^ i^ r^ i> 




c o 




c: o 

oo c c 


- - 


- - 


C - 












-• -: 




-• _• 

^ _• -• -• 



_• ^ 

















o o 




o o 






d d 







o c 





















-H 5i 


-^ «2 Tf 



-1 r' 








>i i>i> 

X '^ C 1< 






X lO 


IC o 


Cl -*< ir; ;s 





-H C^:> 

?0 ir: 



n 1^1 r5 

cor: w ?o 


Tf Tf 

^ •* 




^> or: 

C-. o o o 





c: n 

C: O 

C: Ci 


-ji rr -T -r 

•* -* ^ -ti 





-f -r 

T}1 -t< 



■— ^ 

— ' -^— 

*— Y— ^ — .— 

— . 





1 ; 


11 ; 





1 :: 



• IT" 

,- . _» 










- ■ - 








' — * — > : 





® a 







n3 o 


: c 



"S c ® 


: c 










: is 








. X' 



: j= 







• "? 



; -^ 




C3 S 



.5 ~ .5 










t- -^ 


^ ^ .—1 


■^ - 

1— < 


"" fc, 



O r— 


rS ^ 'C 




o =< 










.3 § 


=i -5 =3 




c3 -S 










n = 






-. ^ >. 


>. ^ >> 



>. -^ 










:3 a 


1— 1 1— 1 


1— 1 

I— 1 





P/«7. il%. S. 5. Vol. 8. No. 47. ^?<^. 1879. 


118 Mr. Piazzi Smyth on Carbon ami Carho-IIydrogen, 


•" tJD 
J= J, 

? O 


"Sd 3 2 

1) 3^ o 
o 0; T 

-■ '"'^ 

n cc ^ 

O) cj aj 

to r-^ 

2 ?^ 
■^ '^ ? 

t< c3 a 









, D 

"^ c5 


-^ C . 

o c 

C - S 

4) — 
. Oj o 

01 I-H 



<JjS i i - 

I- ^ O r. r. c :■: c c: tr c •': r: TO 
X ~ th— ?i -r .-. I- v, — . r- -M -f -3 

-»" 'r:_ »oi-_'- ."_ ■'. ■" 'n '"; --r -^ -^^o 

a a. S -t; 
Jt y C S 

^ 1 >-• 



ir; w -c :c 1: i.n i!t '^ ic lO 

C-J eS I- =: 


t-H ^ S 

1^3 a 









.s c 



; -^ -r ft a ft p ft ft a fi P ft 

•oa^najatiT/T '^' '?T ^ '-~ 'f ^^ CO C5 CI 

X O C-l QC' CO 

CI — ' •ri Ti -r 
-f >r: in ir; o 




CI C'l ci c<» <>J : <?^ 

06000 "6 

: (M : <?! : CI : cq 

•6 ■ 6 -6 -6 

S'tj s-r cr^ cts Cni 

!^^ — _S N"" N"^ ?5 — K -^ N-'-' 
'TS'o'^'^ Sj^ a ^ cS*j rt^ eS^ 

, I- '3 »- 'S 'r '5 J; "3 ii 't3 

; . . . . S &^ £ [i, -S Cm 2 El< i^ &^ 
'Oooofl a c a a 
lfiPfifi'3 '3 '3 "3 '3 
I ci, p^ (i( fJH {x( 

Spectroscoped and Spectromeled in 1879. 


05 CC .^ (M « 

th in 

lO lO O <N 

O -^t^M 

r-( (M!M(M 'M 

<N (M 

C<1(M 5Q-* 



,^ ^ 


X M X 00 o 

C: O t-O 


^ to m l>. O 

!M uo l^ 

o o 


CD t-l> t~t^ 00 


OO 6 




Gi Oi <Xt C^ O"' 


■^^ ^1 ^1 t}^ ^ 


^^ ^^ '^ 'ST^ ^ 

TtH »Oi£5kO 

lO iC lO lO lO 

O lO O »0 lO 

tH '^ ^ ^ 

o 6 6 o i 


6 6 6 6 6 


<o i : 


: '• 




•S5 s 1 
« g a 



6 6 



banco f 
aling a 

6 c 

o c 






<D . . 
13 C O 




let, wi 

;at dii 
in dial 
also pi 

6 c 

d c 



d o 


O u fen's 






^fipfi g hcc^ 






x: S3 a i^ 














: '^ 

CO :c O 





1— < ^- 






^ ,-1 

t- t>. <M 


C5 1?. 

1 c^ 


O t- — 


tt J- 



t- t- OC 



r cr 

r Gs" 

os" e 

O Ci 




-* ^ 

TtH rt< 








: -H 

Tl I'M 

:=P Ir^ 



> -o 

6 -c 


'• <D <0 

■ §'« 




^ k^ 





. e 

1 = 



, ba 



' & 

o ^ 

o i*i a 

,-. o '- 

S © S -ti 


i N 

11 ; 

, o S c. 



© S XI c 



: c3 






(D < 

) O) jj 0. 

O <D 5. 

O "^ 

X g 03t3 




J3 s 

■^ aJ: 




5 fcD 

o '3 n 

o ^ 


1 a 

a "" 

N X 




03 ^ 

= C3 ^ c- 

« cl ^ 

a „ 

c3 ^ S 



^ h 

ra _: 

:.a b-= 

_a _a c 

r' ^ 

J E*»c 2 



^ fc^ 

^ ••-^ s 


>i "z 

3 t. s t 

'3 tl ■? 

^ .^ 

*^ O) c3 o ""^ 




H 3>i 

fe 5ft 


1^ *--^ ^ .i:. 



: u 


a c 





•^ ^^ ti 



^ 1 


c3 r 



c3 -^ ^ 


[ 120 J 

XIV. Note on an Equation in Finite Differences. 
Bij J. J. Sylvester*. 

I GAVE a frroat many years an^o in this Magazine the in- 
tegral of the equation in differences 

U^ = +Ux-2, 


which I obtained by observing that the equation could be 

solved by supposing each u of an odd order to bo equal to the 

u of the order immediately superior, and also by supposing it 

to be equal to the u of the order immediately inferior. The 

upshot of the investigation expressed in the simplest language 

was to furnish two particular integrals of which one gives rise 

to the series 

, 1 1 1 , 1.3 1.3 

Wo=l ?/i = l ?/2 = i ^/3 = i "4 = 2-4 "'^2~4 • • • •' 

the other 

•^ ^ ' '1.3* 1.3 "1.3.5 

See also Boole's Finite Differences, 2nd Edition (editt^d by 
]\rr. Moulton), p. 235. 

Now let ^, a function of any letter t, be the generating 
function of n^. Then, since 

we shall liave 

and integrating we find 

{i-ef (i-o'(i+o-' 
i + < 

— — I we see at a glance gives the values of n^ correspond- 
\V t ) 

ing to the first particular integral ; and since the two first 
terms of the function multiplied by C are l-|-2<, it follows 
that this function is the generatrix of the second particular 
integral — in other words, that 

(1-0^(1 + /)^ 1.3 ^1.3 +13) 

* Communicated by the Author. 

Oa the Laws of Chemical Cliunge. 121 


tsm-^t+ \/\ — £^ 1 r }s\n-H+ V\ — f 

, , 2 , 2.4 4 2.4.6 . 

= ^ + 1- ^- + 0^+17375^ + 

and Integra tin Of 

siu-i^ 2 ^^ , 2.4 t"- , 2A.6t' 

Vl-e 1*3 1.3'5 1.3.57 

Thus we have the remarkable identity 

, 2t 2 
= ^+13 + 1.35 
I do not recollect ever having inet with these remarkable 
series before I discovered them by the preceding method ; but 
on showing them to Dr. Story of this University, he ascer- 
tained that they had been stated not long ago by Mr. Glaisher 
in a paper in the ' Mathematical Messenger,' and made the 
foundation there of various summations for calculating tt ; 
but where Mr, Glaisher found these series, which are not 
given in the ordinary books on the Calculus, or (if new) how 
he lighted upon them, he has not stated, and it is desirable 
that he should do so. 
Johns Hopkins University. 
26th May, 1879. 

XV. On the Laws of Chemical Change — Part II. By John 
J. Hood, Royal Exhibitioner in the Government School of 
Mines, London*. 

WHEN ferrous sulphate in an acid solution is oxidized by 
potassic chlorate, the two salts being in the proportion 
required by the equation 

6FeO + KC103=3Fe203 + KCl, . . . (1) 
I have shown t that the reaction which takes place may be 
very accurately represented by the algebraical equation i/{a + t) 
=b, y being the residue of unoxidized iron after the action 
has continued for t minutes, and ah two constants. 

* Communicated bj' the Author. 
t Phil. Mag. Nov. 1878, p. 371. 

122 Mr. J. J. llood on the Lmos 

In the oxperiments referred to, no account was taken of the 
hydric sulphate present in the solutions, it being merely stjited 
that an indetinite quantity was employed. As this reaction 
seems likely to lead to some interesting facts regarding the 
eflect of salts on rate of oxidation and the like, I have thought 
it advisable to study first the result of a variation in the amount 
and quality of the acid, in order to ascertain in what manner 
the constants in the above equation are connected with the 
conditions of experiment. 

The equation y (a + t) = h was established on the supposition 
that the amount of change in a unit of time was proportional 
to the product of the active bodies ferrous iron and potassic 
chlorate, and that these were in " equivalent '' proportion 
according to (1). 

Since hydric sulphate takes an active part in the oxidation, 
we may suppose from analogy that the amount of change in 
unit of time is proportional to the product of all three sub- 
stances, viz., the iron (A— a), the potassic chlorate (B — /S), 
and the hydric sulphate (C — y), where A, B, C are the quan- 
tities of these bodies at the commencement of the action, ufty 
the amounts that have suflf'ered decomposition up to any time. 

Consequently the equation representing this hypothesis 
will be j„ 

^ = A-(A-«)(B-/3)(C-7), ... (2) 

Taking the chemical equation to be 
6FeS04 + KC103 + 3H2S04=3Fe2(S04)3 + KCl + 3H20,(3) 
for equivalent quantities the follo"sWng ratios will hold : — 

7 1^ 
If, hoAvever, the acid be in large excess, say n times that 
required b}- (3), it may be considered to undergo com})aratively 
little change. Treating it as constant and equal to nv'A, (2) 

replacing (A — a) by ?/ the residue of unoxidizcd iron, and 

__!___, ( c ^ \ 
kWaA ^ \ kvv'nK )' 

^Vriting this equation in the more convenient form 

of Chemical Change. 123 

it is clear that, other conditions being the same, the constant 
h is inversely proportional to the amount of free acid, and a 
represents the number of units of time required to oxidize 
half the original iron. Experiments show a to have this value, 
as may be proved thus : — Let Yobe the value of j/ when ^=0, 

then J= Yoa. When y is reduced to one half, Y^a = -^{a + 1)-, 

therefore a = t. 

Experiments. — The iron solutions employed were prepared 
from ferrous sulphate which had been recrystallized twice, 
and contained about 2 per cent, ferrous iron and 10 per cent, 
hydric sulphate, together with a small quantity of ferric iron. 
When not in use they were kept in an atmosphere of coal-gas. 
The potassic chlorate was repeatedly recrystallized until free 
from chlorides and sulphates. The experiments were gene- 
rally made in sets of four, two Ijlanks containing alwavs the 
same amount of acid, and two having their acid some multiple 
of that in the blanks. The mean values of the constants a, h, 
were then compared. In this way any slight fluctuations in 
the temperature of the water-bath were eliminated. The 
method of making the experiments was as follows : — After all 
the solutions had acquired as nearly as possible the temperature 
of the room, the required amount of hydric sulphate was run 
into a 250-cubic-centim. flask, the iron solution was next 
added, and the whole made up to the mark with distilled water 
that had previously been boiled to expel air. The mixture 
was then decanted into an ordinary flask of about 600 cubic 
centims. capacity and placed in the bath. When the four 
solutions had been made up in this manner, the potassic chlo- 
rate was run in with constant agitation and the time noted to 
two tenths of a minute ; five minutes were added to this reading, 
and taken as ^ = 0. The two observations from each solution 
required for the formula were taken, the first about 8 minutes 
after the addition of the potassic chlorate (or f = 3), and the 
second when about 20 per cent, of the iron had been oxidized. 
The thermometer used was divided into tenths, and could easily 
be read to *05° ; all the burettes, pipettes, kc. were calibrated 
and expressed in terms of each other. 

The first series of experiments (contained in Table I.) were 
performed with the following solutions — 

( ferrous iron 1'735 per cent. 
< ferric 

Ferrous sulphates ferric „ '030 

(free H2SO4 9-86 „ 
Potassic chlorate 1*813 per cent. KCl O3. 

Each experimental solution consisted of 28' 7 cubic centims. 


Mr. J. J. Hood on the Lmos 

iron solution ('4908 grm. Fe), 10 cubic ccntims. potassic 
chlorate solution ("1813 grm. KCIO3), and the necessary 
amount of acid : the total volume in every case was 2G0 cubic 
centims. The permanganate used for iletermining the iron 
was of such a strength that 10 cubic centims. wore equivalent 
to -0199 grm. Fo. 

The numbers a and h in the Table were calculated by the 
equation y {a + t)=b, where y is the number of cubic centims. 
of the permanganate required for 10 cubic centims. of the ex- 
perimental solutions, a' b' are the values for the blanks or 
when 5 gnns. Hg SO4 were used. The ratios are those of the 

means and the acid ;that of — gives the value of?/ when t=0. 

Table I. 












a' : a. 

b' : b. 



























12° -8 ■ 











































































13° -9 














of Chemical Change. 


By an inspection of the above Table it will be seen that 
from 5 to 20 grms. the rate of change is proportional to the 
amount of free acid, above 20 grms. the rate increases more 
rapidly than the acid. This latter fact seems strange ; for it 
might be supposed that when large quantities of acid were 
present the oxidation would suffer comparatively a retardation. 
That this increase of rate in proportion to the acid takes place 
gradually and, apparently, according to some definite law, is 

shown in the curve in the figure, the ordinates representing 
the rate of change and the abscissae the amount of acid. 

Table II. contains the results of a series of experiments with 
the hydric sulphate, ranging from 3 grms. to 20 grms. Each 
experiment consisted of •4988 grm. Fe and -1820 grm. 
KCl O3, 10 cubic centims. of the permanganate being equal to 
•0192 grm. Fe ; total volume 260 cubic centims. The blanks 
are those containing 5 grms. Kg SO4, with which the other ex- 
periments are compared. 


Mr. J. J. Hood on the Ldics 

Tabic 11. 








a. 1 b. 

a' -.a. 

























• -796 





































































Somewliat similar results have been obhiined from various 
chemical reactions. Harcourt and Esson investigated the 
influence of hydric sulphate on the rate of change when oxalic 
acid is decomposed by })otassic permanganate*, and when 
hydric iodide is decomposed by hydric peroxide f; and they 
found that the rate of change dei)ended on the acidity of the 
solutions. So also Boguski and KajanderJ, in their experi- 
ments on the evolution of carbonic dioxide from marble, found 
that the rate at which the gas was given off was proportional 
to the concentration of the acid. 

Effect of Ilydric Chloride. 

A series of experiments were made to find liow much hydric 
chloride was ret][uired to substitute a given weight of hydric 

Phil. Trans. IStU!. 

J5iT. ikiit. chcm. (.Jes. 1877, p. 34. 

Phil. Trails. 1807. 

of Chemical Change. 127 

sulphate to produce the same rate of oxidation as the latter 
acid alone. The values obtained would at first sight seem to 
represent the absolute ratio of the dynamical equivalences of 
these two acids ; but on considering the different changes 
that take place in the two cases, such an inference cannot as 
yet be draAvn from this single reaction. When hydric chlo- 
ride is added to a solution of ferrous sulphate containing free 
hydric sulphate, the colour changes to a light straw-tint, 
owing probably to the formation of some ferrous chloride. 
When this solution is oxidized by potassic chlorate it becomes 
after a time of an orange colour, due to the ferric chloride 
formed ; so that, when experimenting with two solutions, one 
containing hydric sulphate and the other hydric sulphate and 
chloride, in the former case we have ferrous sulphate being 
oxidized to ferric sulphate, and in the latter a mixture of 
ferrous sulphate and chloride (having probabh' different 
facilities of oxidation) converted into ferric sulphate and 
chloride, also an oxidation of the hydric chloride. 

That ferrous sulphate in presence of hydric chloride is 
partly converted into chloride may account for the fact that 
in many cases when about 4 grms. H CI were emploved the 
observed and calculated values for i/ or t were found to differ, 
the reaction seeming to undergo a gradual retardation. These 
discrepancies, however, might arise from the difficulty of 
making sufficiently accurate determinations of the iron by 
permanganate in presence of hydric chloride. 

Various strengths of solutions were tried ; and the numbers 
obtained for the ratio of H Ci to H2 SO4 were invariably the 
same within the limits of experimental error. 

The most complete series of experiments, contained in 
Table III., were made with the following quantities of sub- 
stances : — •5440 grm. iron, "1985 grm. potassic chlorate, and 
various amounts of acid ; total volume 260 cubic centims. ; 
10 cubic centims. of the permanganate equal to '0201 grm. 
of iron. 

The numbers under " calculated ratio of dynamical equiva- 
lence of H CI to HoSO^^' were obtained in the following 
way. It has been shown that b, or, in the first experiment 
with 6 grms. Hg SO4, 2357*5 is inversely proportional to the 
amount of acid ; consequently to give the value 1664*8 it 
would require 8*498 gmas. Hj SO4. But this number w^as 
obtained with 4 grms. H2SO4 and 2 grms. H CI. Hence by 
exchanging 4*498 grms. Ho SO4 for 2 grms. H CI, the same 
rate of change would be produced. Expressed in molecular 
weights, 36*5 parts by weight of hydric chloride are equal to 
82*1 parts of hydric sulphate in the dynamical sense. 


On the Laws oj Clionical C/i<(iiye. 
Table 111. 

Tom p. 




Am 01 

lUt of 


Ratio of 
H CI to 

Calculated ratio 

of dynamical 

equivalence of 

HCl to II, SO^. 














2 ■ 2 


12°-(; . 




















36-5 : 80-9 













365 : 80 
























13°-2 . 


















* 14°-4 





. 36-5:98 

36-5 : 78-7 








* These four experiments were made -n-itb different solutions from the others. 

Taking into consideration the results contained in Tables I. 
and II. *it is evident that the calculated dynamical ratio of 

hydric chloride to sulphate cannot bo correct, since - is not 

exactly proportional to the amount of acid. To find the true 
value a scries of experiments were made with the hydric chlo- 
ride to sulphate ranging from 36'5 : 75 to 36-5 : 85 ; and the 
numbers found to give the same rate of oxidation were 30-5 
parts by weight of hydric chloride in place of 80 parts hydric 
sulphate (experiments nos. 4, 5, 6, Table III.). It is curious 
to note that this is the same as the ratio of the molecular 
weight of hydric chloride (36*5) to that of sulphur trioxide 


Several attempts have been made to obtani the ratio of 
dynamical equivalence of these two acids. Harcourt and 
Esson, with reference to their experiments on the dccoinpo- 

On the Source of Souwl in the Bell Telephone. 129 

sition of HI by HgOs, say*, "Comparing equivalent quanti- 
ties, it had been observed that hydric chloride increases the 
rate of change nearly twice as much as hydric sulphate." 
Ostwaldf, by a series of experiments on specific volumes 

arrives at the conclusion that ^j ^,. =1'93. 

Subsequently Mills and Hogarth ±, after a series of experi- 
ments on the effect of hydric chloride and sulphate on lactin, 
considered Ost\A-ald's result not far from the truth. Taking 
80 as being the correct number for Hg SO4, the above experi- 

3H PI 
ments o-ive for the ratio tt >.^/^-w the value 1"63. 

*= Hg bOi 

In comparing the rates of two different experiments by the 
equation 7/(a + t) = b I have in every case taken the ratio p 
as representing the true value ; but, seeing that a is the time 
required to perform half the oxidation, — should be equal to 

.-. But this is not the case (Tables I. and II.). The reason of 

the discrepancies is, that the value of y in each case is not the 
same when ^ = 0. If in two experiments we calculate the 
times required to reduce ?/, say, from 10 to 5 units, and com- 
pare them, we get the same ratio as p. 

It will be noticed that the constant a is independent of the 
strength of the permanganate used for determining the iron. 

My best thanks are due to Dr. Frankland, in whose labora- 
tory I had the advantage of performing the above experiments. 

XVI. Notes from the Physical Laboratory of University College, 
Bristol. By Prof. Silvanus P. Thompson, B.A.,D.Sc.\ 

I. On the Soiirce of Sound in the Bell Teleplione. 

THE question has been at various times and in sundry 
places discussed whether the sounds emitted by the Bell 
telephone, when used as a receiver of currents, are caused by 
molecular vibrations in the instrument, or are due to vibra- 
tions executed by the thin iron disk as a whole. The former 

* PhU. Trans. 1867, p. 134. 
t Jouni. prakt. Chem. n. F. xvi. p. 419. 
X Proc. Roy. Soc. vol xxviii. p. 272. 

§ Communicated by the Pliysieal Society, having been read at the 
Meeting on April 20, 1879. 

130 Prof. S. P. Tliomi)son on iJie Source 

theory ajipoars to have I )oeii started hy Professor Pell liimself* 
in order to account for the transmission of speech by instru- 
ments having very thick iron diaphragms, and by the instru- 
ments having no diaphragms at all. This view has been also 
upheld by the Comte Uu Moncel in several connnunications 
to the learned societies of France. The other view appears to 
have been first distinctly put forward by Mr. W. H. Preece, 
in introducing the telephone to the British Association at 
Plymouth in 1877t ; and it has for its most vigorous suppor- 
ters M. A. Niaudet} and Colonel Navez, the latter of whom 
has replied more than once to points raised by M. Du Moncel. 
It is a view which appears also to be supported by the recent 
experiments of Professor Hughes. 

The evidence now to be adduced, though not absolutely 
conclusive on the point at issue, opens out several fresh ])oints 
of interest. It consists, in brief, of the results obtained by 
applying to the field of the telephone the experimental method 
of studying the so-called lines of force, originally due to Gil- 
bert, and developed by Faraday. The details of the method 
followed by the present writer are identical with those de- 
scribed in his communication of June 23, 1878, " On Magnetic 
Figures," &c., and which consists in fixing pemianently onto 
glass plates the figures obtained by iron-filings. 

The figures obtained by means of iron-filings were resorted 
to with the view of ascertaining whether the changes in the 
magnetic field of the telephone were sufficiently marked to 
account for the alleged motions executed by the iron diaphragm, 
or whether they were such as to give any support to the mo- 
lecular hypothesis. 

The first step was to investigate the field of a bar-magnet 
when one pole was placed near a thin iron diaphragm. 

It was known at the outset that a thin plate of magnetic 
matter might be magnetized in an enormous variety of ways. 
The masnetism might be distributed on the two faces, or in 
the manner known as lamellar ; or, instead, any two ponits in 
the disk might be taken as conjugate poles ; or any number 
of poles might be introduced ; or, as in the magnets of M. 
Duter, the magnetization might be radially distributed, the 
central portion having one polarity, the other polarity existing 
all round the circumference. De Haldat showed that a variety 
of irregular magnetizations might be produced by touching 

* A. Graham Bell, " Researches in Electric Telephony," Journ. Soc. 
Telegr. Eng. 1878, p. 414, vol, vi. 

t Rep. Brit. Assoc. 1877, Plymouth, p. 13, W. II. Rreece, C.E., "On 
the Telephone." 

X Telephones et Phonographes, p. 92. 

of Sound in the Bell Teleplione. 131 

steel plates with the pole of a powerful magnet ; and the pre- 
sent author also found analogous etfects to be produced by 
passing currents through steel disks. It therefore became a 
matter of some interest to determine the character of the mag- 
netization of the telephone-disk. 

The figures exhibited two unsuspected features : — first, that 
when the diaphragm is larger than the end-face of the magnet, 
and even when it does not touch it, the distribution of the 
magnetism induced in the diaphragm is partially lamellar in 
character, partially radial. The central portion is magne- 
tized almost entirely normally to its plane ; the exterior por- 
tion is radially magnetized — a narrow annular region lying 
between these, in which the character of the magnetization 
is mixed. It was further observed that this neutral zone is 
of greater diameter when a larger magnet is employed, and 
that it enlarges also as the distance separating the magnet 
and the diaphragm is increased. It is more strongly marked 
as a region of separation between the central lamellar portion 
and the outer radially magnetized portion in the diaphragms 
of thin material than in those of thick. The position of this 
neutral annular zone is marked in fig. 1 (p. 132), which is 
a sectional diagram compiled from the figures produced by 
filings, by a point of flexure in one of the " lines offeree " pro- 
ceeding from the pole towards the diaphragm. The second 
feature noticed was that some of the outermost lines of force 
ran round to the front of the disk, entering it very near its 

The next effect to be studied was that pi-oduced by the 
magnetic inductive action of a current traversing a coil of 
wire about the pole. For the convenience of obtaining the 
filing-figures upon glass plates but one turn of wire was em- 
ployed, passing through holes drilled in the glass, and situated 
as is the coil in the Bell telephone over the pole of the mag- 
net, the position arbitrarily found the most efficient in the 
construction of that instrument. In almost all modern ele- 
mentary treatises on electromagnetics it is shown that the field 
of a plane closed circuit is equivalent to that of a lamellar 
magnetic shell of equal strength, or one which has an equal 
number of lines of force passing through the area it occupies. 
The result of passing the current around the pole of the mag- 
net will therefore be, so far as the field in the plane of the coil 
is concerned, to increase or diminish respectively the number 
of lines of force due to the magnet by the number of lines of 
force due to the closed circuit, according as the direction of its 
field coincides with, or opposes that of the magnet. But the 
action is not so simple on the regions of the field outside the 

132 Pri)!". S. V. Tlu)ni|»son on tJie Source 

])lane of the circuit. The direct ion as well as the mnnber 


lines of force may be altered, and this in a manner so complex 
as almost to defy calculation, especially if the mutual induc- 
tion between this magnetic combination and the adjacent iron 
disk be taken into account. The figures obtained with filings 
when the current traversed the circuit in op])osite directions 
(see figs. 2 and 3) show that the lines of ibrce proceeding 

I'i-. 1. 

mm Fip:. 2. 

Fi<r. 3. 

outwards from the pole wore in fact thus altered both in 
number and in direction, and that, in addition to strength- 
ening or weakening the field, the passage of the current had 
the effect of apparently thrusting the lines of filings forwards 
towards the iron disk or backwards from it. Moreover thts 
region separating the two separate distributions of magnetism 
on the diaphragm was shifted on the passage of the current — 

of Sound in the Bell Telephone. 133 

being contracted in diameter when the current reinforced the 
magnetism of the pole, becoming enlarged when it passed in 
the opposite sense. 

Knowing from the experiments of Joule and De la Rive 
that a portion of iron, when magnetized in a particular direc- 
tion, grows longer in that direction and shorter in its trans- 
verse dimension, let us deduce what the etfect will be on 
the diaphragm of a telephone of these two species of mag- 
netization. If the m ignetization were radial, the tendency 
would undoubtedly be, supposing the disk clamped circum- 
ferentially, to thrust the middle point of the disk backwards 
towards the magnet, and to give it a conical shape. If the 
magnetization, on the other hand, were lamellar, the tendency 
would be to make the diaphragm thicker, and to contract it 
over the area thus magnetized. In the actual case where the 
magnetization partakes of both characters, the two distribu- 
tions being separated by a neutral zone, the tendency to each 
form would exist over the regions respectively atfected. But 
the extent of these regions varies with the varvino- induction 
of the currents in the coil. Hence, while the total attraction 
varies, giving rise to oscillations of the diaphragm as a whole, 
the neutral annular line will also be. continually sliifting its 
position and predisposing the diaphragm to take up new nodal 
forms of vibration, thereby rendering the timbre corresponding 
to the complicated undulations of the currents arriving from 
the transmitter. 

The result obtained may be regarded from another point of 
view. If a slight displacement of the iron disk, though unable 
to aflfect to any appreciable extent the strength of the magnetic 
field as a whole, alters its strength at any one point or in any 
narrow region, or if, even without altering the average num- 
ber of lines of force in any part of the field, such a displace- 
ment shifts the position of some of the lines of force across 
a narrow region of the field, it mav still exercise a consider- 
able inductive action on a closed coil of wire lying in the 
region where the amount of shifting is greatest. For, since 
the induced electromotive force in a closed circuit is not pro- 
portional to the strength on an invariable magnetic field in 
which it lies, nor yet to all changes in its strength, but only 
to such changes as cause a greater or less number of lines of 
force to j)ass through the area within the closed circuit, it is 
evident that the inductive action will be strongest in coils of 
wire v.-hich lie in the region Avhere there is most change in the 
direction of the lines of force. We have here the rationale of 
the empirical practice of the constructors of the telephone 
alluded to above — namely, that of using only a small coil of 

Phil. Mag. S. 5. Vol. 8. Xo. 47. Aug. 1879. L 

134 Dr. S. P. Thompson on Mar/netic Figures, and 

wire, and winding it upon a narrow bobbin placed upon the 
extremity of the magnet. 

Conversely, the passage of a very feeble current through a 
coil so placed will j)roduce a greater change in the effective 
intensity of the magnetic tield Ixitween the core and the dia- 
phragm than would l)e produced by the same current traver- 
sing a similar coil in any other region of the field ; for here it 
has its greatest power to shift the position of the neutral zone, 
and to alter the distribution of magnetism in the diaphragm. 

It would therefore appear unnecessary to form an hypo- 
thesis of molecular vibrations in the disk to account for the 
emission of sounds by the instrument. Such vibrations do in 
fact exist ; but their existence does not necessarily prove that 
they play any important part in the production of the sound. 
And it must be remembered that, so far as the disk is con- 
cerned, they take place within the narrow range of the extreme 
positions possible to the neutral annular zone. 

Two further experiments seem to confirm the conclusion 
derived from the foregoing observations. If a compound dia- 
phragm be used, consisting of concentric annuli of thin iron 
fixed to a stretched membrane of paper, or if a small iron disk 
thus fixed be employed, as in Bell's earliest experiment and in 
some of the experimental telephones of M. Niaudet, a curious 
timbre is thereby imported into the voices of speakers, though 
their enunciation is very distinct. A similar result is found 
to follow the employment of small thick diaphragms. In each 
of these cases the disposition favours the lamellar distribution 
of the magnetism. 

If, however, a compound diaphragm be employed, consisting 
of a number of radial pieces similarly fastened to a stretched 
membrane, tones are well rendered, but enunciation is not 
distinct. This result is also obtained when the diaphragm of 
iron is too large in proportion to its thickness. In these cases 
the greater part of the magnetism is radially distributed. 

Whenever a complete theory of the telephone is framed, 
these are points which must be taken into account. 

II. On a new Variety of Magnetic Figures. 

De Haldat showed that it was possible to produce magnetic 
writing upon a steel plate by actually writing with the pointed 
pole of a powerful magnet, the writing being invisible until 
fine iron-filings were dusted over the plate. In the Physical 
Laboratory of LFniversity College, Bristol, a small circular saw 
has been found to afi'ord a j)late of suitable thickness and 
quality to produce good results. The latent characters re- 
mained for eiirht months after beiufi inscribed. 

the Magnetic Behaviour of fixed Iron Filings. 135 

While experimenting with these figures, it occurred to the 
author to try the effect of leading the current of a poAverful 
battery into the plate and of writing on it with the other pole. 
This done, tine iron-filings were dusted over the plate ; and on 
gently tapping it the writing became legible immediately. A 
small thin disk of steel which thus had a current passed through 
its centre exhibited afterwards a magnetism distributed in 
small concentric rings. 

III. On Magnetic Figures for Demonstration. 

For the production of magnetic figures filings of wrought 
iron are usually employed, though cast iron answers fiiirly. 
Finely powdered magnetic oxide is recommended by some 
wu-iters, though it does not appear that its employment is 
attended Avith any great adyantage. Professor A. M. Mayer 
took special pains* to produce filings of eyen quality from 
specially prepared Norwegian iron; but he says nothing about 
the size of filings he found best suited for the purpose. Fa- 
raday made the remark f that " large and also fine filings are 
equally useful in turn." 

The author, desiring to obtain figures on a larger scale than 

• TIP 

usual, for purposes of class demonstration, used a number ot 
small steel needles with success. In the case of thin elongated 
bodies such as these, the magnetic moment is great as com- 
pared with the mass; hence it was to be expected that filaments 
of fine soft iron wire would also yield a good result. Accord- 
ingly he had a quantity of fine iron wire gauze of 32 meshes 
to the inch cut to fragments. The filaments thus produced 
were scattered in the usual way by means of a pepper-box with 
perforated lid. The figures giyen by these filaments with 
large magnets possess yery well-marked characters, and are 
decidedly superior to those made with ordinary filings. 

IV. On the Magnetic Behaviour of fixed Iron Filings. 
Haying occasion to draw the attention of his students to 
the property of the lines of magnetic force as being at eyery 
point tangential to the position of a small freely-suspended 
magnet placed aboye them, the author, placing thus a small 
magnet over the filings fixed some time previously to glass, 
and from which the magnet producing them had been removed, 
noticed .that they still retained their magnetic property. It 
then occurred to him to see whether they still possessed direc- 
tive force as a whole, and found that they appeared capable of 
attracting and repelling a lightly suspended needle. A figure 

* Vide American Journal of Science, 1872. 
t 'Experimental Eesearche?/ vol. iii. p. 398. 

136 Mr. J. H. Bicket on the 

produced by a single bai--inaf(net and fixed permanently to a 
slip of card by ^uin was suspended li^^htly u{)on a needle- 
point by means of a ^lass cap. It set itself in the magnetic 
meridian, and was found capable of being deflected on the ap- 
proach of a steel magnet. The fixed magnetic curves are 
therefore themselves mao-iiets. 

V. Magnetic Figures of three dimensions. 

The writer has several times essayed to produce magnetic 
figures of three dimensions. The ditiiculty in producing them 
arises from the weight of the iron filings when unsupported, 
as they must be when the whole figure does not lie in one ho- 
rizontal plane. With even the most powerful electromagnets 
the forms of the curves cannot be actually constructed in iron 
filings for more than a few millimetres length. 

Attempts to float iron filings are also ditiieult, as there is 
no transparent liquid nearly approaching the density of iron. 
The writer has tried heavy jjarafiins and strong solutions of 
mercuric iodide in potassic iodide. Better efiects were ob- 
tained, however, when iron filings were employed which had 
previously been coated with shellac varnish, and which there- 
tore possessed greater buoyancy. The experiment is curious ; 
but the ditiiculty of seeing across the forests of lines of filings 
reduces the observation to one of curiosity only. 

Another process attempted consisted in plunging a small 
magnet into a soft paste of plaster of Paris and iron filings. The 
])laster shortly hardened ; and then sections were cut in various 
directions. The figures observed, however, were poor ; and 
no observations were made of any additional interest as the 
result of the attempt. 

XVII. On the Dissociation of Aniline Colours. By J. H. 
Bicket, Assistant in the " Young " Lahovatorg of Tech- 
nical Chemistry, Glasgow*. 

IN the course of their researches on dyeing, an account of 
which has recently been connnunicated to the Chemical 
Society t, it was found by Professor Mills and Mr. Thomson 
that a dilute aqueous solution of rosaniline acetate or hydro- 
chloride is entirely decolorized by boiling, nevertheless im- 
parting the rosaniline salt in its normal red state to apiece of 
silk immersed in the heated liqued On Professor Mills's 
suggestion, I have made some further experiments in con- 
nexion with this subject. 

* Communicated, bv Dr. Mills, F.K.S. 
t ' Journal ' (1879)', i. p. 20. 

Dissociation of Aniline Colours. 137 

I. Rosaniline. 

300 cubic centims. of a solution of rosaniline acetate or liy- 
drochloride containing "0003 gnn. in a litre of water are com- 
pletely decolorized by balf an hour's heating to ebullition ; 
15 cubic centims. of this solution lose their colour in a few 
minutes. Either of these bleached solutions will then readily 
impart unaltered colouring-matter to a piece of immersed 

In order to ayoid r.:iy possible bleaching effect due to any 
alkali that might be extracted from glass yessels by a boiling 
aqueous fluid, an experiment was made in a large platinum 
dish, with precisely the same results as before. We are there- 
fore clearly dealing with a real case of dissociation, »the rosa- 
niline and its Imlric acetate (or chloride) remaining in pre- 
sence of one another Avithout combination. In this respect 
these salts well maintain their known general analogy with 

In order to ascertain whether the dissociation would be re- 
yersed by prolonged preservation at the ordinary temperature, 
some of the bleached liquid was cooled, set aside, and observed 
from day to day. At the end of thirty days a considerable 
proportion of the colour somewhat suddenly returned. 

The success of this experiment naturally induced me to try 
the effect of cooling the liquid, as a means of accelerating the 
return of the colour. Some of it was placed in a tube and 
cooled down to — 17'^ C, when it of course solidified; the 
solid mass, when thawed, had a decided red colour. 

The colour of the boiling liquid is restored, as might have 
been expected, by addition of a trace of acid. The tempera- 
ture of boiling water appears to be that at which, in this case, 
complete dissociation is best effected. 

II. Mauveine. 

A solution of mauveine acetate, of the same strength as in 
(I.), is bleached, by boiling, in much the same time as that of 
rosaniline. A solution of double that strength refuses to 
bleach, even when-boiled for several hours. Silk immersed in 
the boiling decolorized liquid is immediately dyed. The colour 
can be restored, and the dissociation therefore reversed, either 
by freezing or by keeping at the ordinary temperature for several 
days; and the colour of the hoiJing liquid can be again brought 
out by addition of a trace of hydric salt. 

III. jyicholsons Slue. 
Unlike the preceding salts of amines, Xicholson's blue is a 

138 Dr. F. Auerbach on the Passage of 

sulphonic compound, having, as a rule, the formula 

C20 Hie (Ce H,)2 . a H4 N3 [NaSOa]. 
Our own sample, which was prepared many years ago, may 
possibly have contained a little of the disulphonic compound. 
The solution which I employed contained '1 grm. in a litre, 
being therefore three hundred times as strong as in I. and II. 
When this was boiled, even for several hours, it refused to 
bleach ; but on allowing the hot li(iuid to cool gradually, the 
colour slowly faded away before the ordinary teinperature was 
reached. Repeated attempts to decolorize the liquid by heat- 
ing to temperatures short of 100° were all attended with 

When the decolorized liquid was. kept for three or four 
hours, or frozen, or mixed wdth a little hydric acetate, the 
colour was restored. 

The dissociation-temperature for Nicholson's blue is obvi- 
ously a little below the boiling-point of water. 

Phenomena of bleaching in connexion with Nicholson's 
blue were first noticed by my friend Mr. Louis Campbell. 

XVIII. On the Passage of the Galvanic Current through Iron. 
By Felix Auerbach, Ph.D., of Breslaii. 

[Continued from p. 18.] 
§ 7. HTN the following I will endeavour to elucidate the ob- 
J- served phenomena on the basis of the theory of rotable 
molecular magnets. In so doing I make use of the conception of 
?i-orX:, defining it for the present case as the product obtained when 
the force lohich must be overcome for the rotation of a molecular 
magnet is multiplied by the angular quantity of that rotation. 
The extra currents arising in iron have already been commonly 
recognized as the expression of such performance of work. 
When, from a fixed moment onwards, a current generated by 
a constant electromotive force performs work which till then 
it did not perform, then Ohm's law is valid only on the hypo- 
thesis that either the current-intensity i or the resistance 10 
obtaiiis another value. Assuming the former case, the equa- 
tion is usually written 


e ^r— 

(I of *. 


1 V 

that is, the quantity - --.- (in which a denotes the value of the 

* Helmholtz, Die Erhnltuny der Kraft : Berlin, 1847. 

the Galvanic Current through Iron. 139 

work of the unit of heat, V the potential, for instance, of the 
unit current on the magnet in reference to which work is per- 
formed) is regarded as a new electromotive force which coun- 
teracts the first. But I do not see why it is not also admissible 
to write 

•_ ^ 

where w'a denotes a new resistance added to w in consequence 
of the external work*. At all events it cannot be proved, as 
Colleyt will have it, that the latter equation is false. Colley 
thinks himself authorized to conclude as follows: — If Tand T^ 
denote the times necessary, with and without the performance 
of work, to dissolve 1 gram of zinc in the galvanic series, then, 
if 10 varies, 

'' T' + ^T^ (1) 

where g signifies the work done in the unit of time. Now, 

-T = — ^—T; (2) 


e=e+'^^(iv + u'j,), 

which is impossible. 

Equation (1) is true ; but equation (2) is as little applicable 
as in the other case (where e is considered variable) the cor- 
responding equation 

-T=^^T', (2a) 

where e signifies the variation of e. Much rather are both 
equations to be rej^laced l)y the common equation 

T = T', (3) 

which expresses that with i the evolution of heat has also di- 
minished ; and this leads, in our case, to the very possible 

e e 

W 10 + Wa 

from which we cret 

«"A= -2^^— (^A) 

e — loq ^ 

* But compare Wiedemann, Galv. ii. 2, p. o21, 
t Pogg. Ann. clvii. p. 370 (1876). 

140 Dr. F. Auerbacli on the Passorje of 


q=: /'"'^ , (4b) 

This eciuation can be readily verified if •\ve pursue the extra 
current which arises at the closing of a known current, if the 
current deflects a inan;netic needle of known moment, and if, 
besides, the horizontal component of the intensity of the earth's 
mafjnetism is known*. 

In recrard to practice it is at all events most convenient, 
■whenever Avork is ])erformed, -whether momentary or lasting, 
to admit an alteration of the resistance. 

Accordingly t/ie resistance of an iron icirein the first moment 
after the closing must he greater, in the first moment after the 
opening it must he less, than during the rest of the time that the 
current lasts. For then the molecular magnets, in consequence 
of the directing force of the current, shift into a position more 
or less approximating to the circular arrangement when the 
current has to perform work in relation to the direction-force 
of the molecules. Here the molecules return more or less into 
their natural position ; the direction-force therefore does work 
in regard to the current. With this the observations are in 
complete accordance. 

As soon as that actual energy which the molecular magnets 
receive from the rotating force of the current is entirely con- 
verted into potential, the current has no more work to perform 
■svith respect to the direction of the molecular magnets. Hence 
we could not but conclude that the resistance Avould now take 
its true value, corresponding to the iron wire at rest internally 
(or in a determined thermal motion), if we had not to bear in 
mind that through the action of the rotating forces exerted by 
the current the internal state of the iron (as may also be ima- 
gined) has become different, and remains so till the current is 
interrupted. Accordingly the iron might possess two different 
resistances, of which one only, viz. that of the circularly mag- 

* That even in the case represented by M. CoUey (e variable) equa- 
tion (2 A) is not applicable may be inferred from its leadin<i: to a contra- 
diction. For M. Colley arrives by correct conclusions at the equation 
(con-esponding to eq. 4 b) 


9= -, 


which cannot be true, since for t indefinitely small it yields 

ecle . , , » 2e de 
q= — instead of o= : 

IV w 

while if in this case also, as above, we make use of eq. (3), it brings us to 
the last-mentioned, the true equation. 

the Galvanic Current through Iron. 141 

netized iron, vould be at once accessible to obsenation, while 
the other, resistance of the unmagnetic, would have an im- 
portant theoretic signification, inasmuch as it alone is compa- 
rable with the quantities which in other metals we bluntly call 
the resistance. 

Assuming, then, that these two quantities indeed differ (and 
experience shows that this is the case), yet no way based on 
special conclusions can be imagined in which we could decide 
which is the greater. In such cases considerations having for 
their starting-point the principle of the conservation of force have 
recently been frequently ap]jlied with success. Taking the 
same course, I place first of all a general principle which 
results therefrom, and which hitherto, so far as is known to 
me, has been expressed only for special cases. It is : — 

No force can of itself bring in conditions more favourable for 
its own action tlian tliose ivliich it meets ivith. 

This needs no explanation; even the expression "of itself* 
has become iniiversally familiar since it was introduced by 
Clausius*. The proposition in which he first made use of it, 
" Heat can never of itself pass over from a colder into a hotter 
body," is itself a special case of the above principle. Another 
is Lenz's law which determines the direction of the induced 
current. Further, here belong the facts that in solids the 
cubic coefficient of compression diminishes as the pressure in- 
creases, that the specific heat and the galvanic resistance of 
solid bodies increase with the temperature, &c. 

For the present case we may conclude from the above prin- 
ciple that the resistance of iron as observed by us when a cur- 
rent is conducted through it is greater than that ideal value. 
Thence, in the next jdace, it follows that circularly magnetized 
possesses a greater resistance than unmagnetic iron, at least 
if the amount of the circular magnetization does not exceed 
that which the current itself could produce. Evidently, how- 
ever, we may drop this limitation ; for if the circular magne- 
tization be greater than the current itself can generate, yet 
there is always another intensity of current possessing this 
property. For this latter, therefore, the above proposition 
holds good. But the resistance of an iron wire possessing a 
definite magnetic state] is independent of the intensity of the 
current ; consequently that principle is valid for any amount 
of circular magnetization. 

It follows, further, that the resistance must be lessened by 
feeble longitudinal magnetizings. For, according to the above, 
we may assume that circularly magnetic iron conducts the 

* Die mechanische Wdrmthenrie, i. p. 81. 

t That this addition is necessary, will be shown in § 8. 

142 Dr. F. Auerbacb 0)i t/ie Passage of 

current the worse tlio more intense the circular magnetization 
is ; but by the added longitudinal magnetization a portion of 
the circular is annulled. In fact my experiments show, in 
iron as well as in steel, a diminution of the resistance in con- 
sequence of feeble magnetizings. 

The beliaviour is ditterent Avhen the longitudinally magne- 
tizing force is great ; a longitudinal magnetizing will then 
result from its cooperation Avith the circular magnetizing force 
of the principal current. And here the theory leaves a blank. 
The resistance of longitudinally magnetized iron can be less 
or greater than that of the unmagnetic. In the former case 
the resistance-function has nowhere a minimum or a maximum ; 
but rather tlie resistance constanthj rises from tlie state of satu- 
rated longitudinal magnetism to the state of saturated circidar 
magnetism : this case is realized, as the experiments show, in 
hard steel. In the other case the resistance-function has a mi- 
nimum vcdne for the vnmagnetic state ; my experiments have 
in fact yielded this result in iron and soft steel : here, to one 
and the same ordinate of the resistance-curve two abscissa3 
correspond; that is, two magnetic states (namely, longitudi- 
nally and circularly magnetic) correspond to the same resis- 
tance. The conjectural form of the resistance-curves is repre- 
sented in PL I. fig. 2. This gives the explanatison of experi- 
ments 7, 21, and 25, both so for as their result Avere positive, 
and also so far as thev were neofative. Bv makin<T use of the 
laws laid down res])ecting magnetization by a circular current 
or by a spiral*, and respecting circular magnetization by the 
current flowing through the wire itselff, we can calculate what 
must be the ratio of the electromotive forces of the magneti- 
zing and of the principal current (that is, the ratio IM : H) at 
given values of n, ic^, I, and d, in order that 8 (for iron and 
soft steel) may vanish. But as the smallness of the values of 
S hardly permits this calculation to be tested, I forbear to 
carry it out. I will only mention that, according to the ex- 
periments, that ratio appears to depend not only on n, iCo, I, 
and (/, but also on the nature of the wire. That the depen- 
dence on the thickness is considerable can be made evident by 
the followin Of consideration. The Ion oitudinallv mamietic mo- 
mcnt taken by the wire is, with equal magnetizing forces, 
nearly proportional to the square root of the thickness!]:. The 
case is different with the circularly magnetic moment ; indeed, 
with equal magnetizing force the circularly magnetic moment 
appears not to depend essentially on the thickness: but the 

• Conf. Wiedemann, Gah. ii. 1, pp. 180, 320. 

t Streiutz, /. r. 

X Dub, Ekdromagnetismtts (1861 ), p. 197. 

the Galvanic Current through Iron. 143 

magnetizing force varies considerably Avith tlie thickness ; for 
it is 


\ \ ^Mrdldcf). 

Integrating, and using the equation 



in which / signifies the specific resistance of iron, wc get for 
the magnetic moment : — 


where <^((t) is a complete function of d, slowly varying as d 
varies, and in the same direction, and '^{l) is a function of I 
which is of no consequence here. For larger values of I, at 
least if that of d is not too great, we can so arrange that tt'^ 
may be neglected ; we then find : — 

K= const. Hr/^(/)((0.>^(0- 

But even when d is so great that conversely -^ can be neg- 
lected against iCk, still 

K= const. 'Ed(})(d) . /■^(O? 
while yet, as mentioned, the longitudinally magnetic moment is 

K'= const. M;iv/rf;^(/). 

As the expression of the work done by the current in the 
rotation of the molecular magnets, an extra current occurs at 
the closing of the principal current, as we have seen, or, as it 
was expressed, a passing augmentation of the resistance. If 
the wire has been previously magnetized longitudinally, and 
is still in that state at the closing of the principal current, the 
rotation by the latter is of course much less. From this wo 
might at first be inclined to conclude that the work also is less, 
which would be contradicted by the observed fact that the 
extra current is in this case more intense. But we must bear 
in mind that the rotation is smaller in amount because the lon- 
gitudinally magnetizing force holds back the molecules more 
strongly than the direction-force, which alone, in the first case, 
counteracted the force of the principal current, but the other 
factor of the product representing the work, the longitudinally 

144 Dr. F. Auerbacli on the Passage of 

magnetizing force, is much greater tlian the direction-force. 
Now, as long as the rotations are infinitesimal, the force varies 
in inverse ])rc)])ortion to the angle of rotation; therefore the 
work of the current remains;mt ; but when the longitu- 
dinally magnetizing force is considerable, and therefore the 
rotations into tlie axial position cannot be regarded as infini- 
tesimal, the work to be done by the current increases, although 
the circular turning produced by it is less. If, to demonstrate 
this, we denote by D the direction-force, by H the directing 
force of the ])rincij)al current, we get (first, apart from a lon- 
gitudinal magnetizing), for tlie work to be done for any one 
molecule in rotating it the angle yjr: — 

A= j Dsm-^dylf. 

Now, if the direction of D for this molecule makes with the 

axis of the wire the angle ^, then -yjr is determined by the 


D sin i/r = M cos (^ + yjr), 

from which follows 

H cos d) 
tan -ylr = -pr — ^t • i' 
^ D + H sm <^ 

Inserting this value in the equation 

A = D(l-cos-»/r), 

we find 


where W denotes the quantity + V I)'- + 2HD sin (f> + IP. 

If now we would describe rigorously the phenomena of the 
extra currents, we have to solve the following problems: — 

(1) What is the mean value of A for all the molecules of 
the wire ? 

(2) What is the amount of the corresponding work for one 
molecule, on which, beside the forces D and H, the force M 
acts perpendicular to H ? 

(3) What is the mean value of this work for all the mole- 
cules ? 

I have prosecuted this calculation under the following 
assumptions : — (a) In the unmagnetic state, all the values of 


<f) between and are represented with equal frequency ; 


values between ^ and tt appeared to me, on account of the 

the Galvanic Current through Iron. 145 

unstable equilibrium which would then of necessity prevail in 
certain parts of the wire, very unlikely ; moreover the value 
of the integral, so far as it comes into consideration, is inde- 
pendent of these, (h) The differences of direction of the mo- 
lecules will quickly diminish with M increasing, consequently 
with diminishing deviation from the axis of the wire : that is, 
the integral which, divided by the ditterence of its hmits, re- 
presents that mean value will be included within limits rapidly 
approaching one another, and at values of 31 which are great 
in comparison with D can be replaced by a ditFerential, and 
consequently that quotient by a differential quotient ; the final 
value of it then represents the.extreme value of the work of the 
current for saturated longitudinal mao;netism. 

The work is, in the second case, greater than in the first, 
from two causes : — first, because the work increases with the 
force to be overcome; an understanding of this can be obtained, 
without a knowledge of those general expressions, in the fol- 
lowing manner: we have 

BA_ 2D + Hsm^ D(D + Hsin(^)- 


BA_ D + H sin (j) DH-cos2 

Kow W can be written in the form 

W = V (D + H sin )- + H' cos^ <^. 
Hence the sum to be subtracted from 1 in the expression for 
^j=) ^s greatest just when 

D + H sin = H cos (f> ; 
and in this case it is equal to 

1 + 1 = 1 

2 ' 2 — -*■• 

Thence it follows that ^r-- is never <0. (We can also brinor 

BA o^ 

^-p^ into the form 

. _ (D + H sin (f>y + 2H^ D cos- (/> + g sin < f> cos^ 4> 

from which we bring out the same conclusion by the develop- 
ment of W.) 

But what has here been proved for ^~ holds also for ^^, 

146 Dr. F. AnorLacli oit the Passage of 

ill case D is very small in comparison with M ; for tlio lonf^i- 
tudinally ma^rnetizing force is of the same nature as the direc- 
tion-force. This is one reason why the work of the current 
for longitudinally ma(]jnetizod is greater than for unmagnetic 
iron. But even wlirn the force to be overcome is the same, 
the work is greater as soon as the an<ile between the direction 
ot the force which does the work and the direction of the mo- 
lecule at the commencement of the performance of work is 
greater. I will calculate at least the upper limit of this varia- 
tion. Thus, let the molecule form with the axis the angle (f) ; 
the first time let H act immediately and magnetize completely 

(that is, let the angle of rotation -yjr ho =3 — ^) ; let this work 


be Ai. The next time let M act first and magnetize com- 
pletely, and consequently rotate through ^ ; then let H act 

and on its part magnetize completely, rotating through - ; let 

A A 

this Avork be ~. The ratio ~ can, evidentlv, never become 
Ai Ai 

greater than in this case, in wliich M is of a higher order than 
D, H of a higher order than M. Now 

Ai = D(l-sin(/,), A2 = D; 

therefore the mean values 

[A:] = ^^ fa -sin </,)#= ^^D, 
[A.]= D; 



f^^ = -^ = 2-752 

Therefore, if M increases, A increases more rapidly than 

]M : — first, because, with continually greater accuracy, D can 

be neglected in comparison with JM," and hence the above for- 

mula for ^-p: becomes continually more strictly applicable ; 

and, secondly, because the longitudinally magnetic state itself 
ex(M-ts a reaction, which, in rough approximation, can be taken 
into account by adding to A a factor constantly increasing in 

value with M from 1 to 2*752 "Whoever, up to these 

data, examines the observations that have been made on the 
extra currents, will find them qualitatively (and, as far as this 


the Galvanic Current through Iron. 147 

is possible with the aA'erage insignificance of the deflections in 
general occurring, also quantitatively) verified. 

I have characterized the extra currents in iron as the ex- 
pression of the work of rotation, and described this Avork by 
an increase or a diminution of resistance. The value of the 
resistance corresponding to the closing current does not sud- 
denly change into the value conditioned by the passage of a 
constant current or a permanent magnetization (or both 
together), but is mostly connected with it by a phenomenon of 
afteraction. Even of the nature of this, from the above an 
idea can easily be formed. If, beside the direction-force, only 
the principal current acts, it imparts to the molecules a rota- 
tion-velocity which, according to the value of H, is constantly 
positive (rotation) or periodically changes its sign (oscillation). 
Now, if even in a magnetic needle moving in a copper shell 
we observe a rapid conversion of the motion of the mass into 
thermal motion, the same conversion will result much more 
rapidly. still in a molecule of an iron wire. A heating there- 
fore takes place, which is only gradually equalized by conduc- 
tion and radiation ; and the e.vpression of this heating is the 
phenomenon of afteraction. In fact, heat is generated not 
merely by longitudinal, but (as Villari* has shown), also by 
circular magnetizing. Into this I do not further enter; I will 
only mention that the series of experiments 16-18 of § 4 and 
the remarks (p. IG) in § 5 apply here. That in those experi- 
ments not only D and H, but also M acted, has, it is self- 
evident, no essential influence upon the result. I add a few 
numbers characteristic of the course of this kind of afterac- 

(1) M = 2B, H=1D, n = 150. These numbers were chosen 
so that S was nearly = 0. Wire y^. The principal current 
was closed after the magnetizing current, t denotes the time 
between two observations. On account of the considerable 
distance of the magnetizing current, some seconds mostly 
elapsed between the closing or opening of the magnetizing cur- 
rent and the first observation ; hence the absolute alteration 
of resistance in consequence of the rotation-work cannot be 
inferred from the numbers, s denotes closing, 6 opening of 
the magnetizing current. The ratios are graphically repre- 
sented in PI. I. fig. 3 ; the reinforced parts of the drawing 
correspond to afteractions. 

It will be seen that at the opening the duration of the after- 
action is less than at the closing. 

* Xuovo Cim. (2) iv. Nov.-Dec. 1870. 


Dr. F. Auerbacb on the Passage of 

Duration of the after- 




At closing. 

At opening. 








No afteraction. 















} -■■ 



\ 30" 



















\ 50" 





} 30" 









\ 50" 








No afteraction. 

Mean ... 



(2) Without magnetizing. H = 2D. A thick soft-steel 
wire, Fg. The bridge in which was placed the galvanometer, 
the current being closed, and the current, the bridge being 
closed, were alternately closed and opened. In the tirst case 
there cannot in general be any extra current. (The weaken- 
ing of the current in the wire by branching otF into the galva- 
nometer cannot, in my arrangement, have had any perceptible 
influence.) In the second case, on the contrary, the full 
current enters into the phenomenon. It was not powerful ; 
nevertheless the afteraction was great. This was shown in the 
following way : — In the tirst case occurred a first excursion 
s-i and a definitive deviation ?<i ; the two stood to one another 
in a constant ratio, conditioned only by the nature of the 
galvanometer-needle and the damping. In the second case 
an excursion .>^2 occurred, greater than Si, and, just as the 
needle had finished its periodic oscillations, a deviation j/j, 
likewise greater than ?/i, which sank only gradually to Ui. In 
the Table, each row contains two experiments, viz. one of 
each sort. 

M' + u'i- was =0'2380. 

the Galvanic Current through Iron. 


Siuts to 











































Of the slow increase of all the uumbei's from experiment to 
experiment I shall speak presently. 

Here belong also some facts already alluded to: — thus 
the phenomenon that, even in the cases in which the mag- 
netizing diminishes the resistance, the first experiment gives 
the opposite result ; for the evolution of heat occasioned by 
friction in the performance of work continues to operate. 
Further, the opening has often an influence in the opposite 
direction : that is, the resistance is lessened by ma^netizino: 
where otherwise it would be augmented, or is more strongly 
depressed than it would other\vise be. This phenomenon ap- 
pears especially striking on the reversal of the current (com- 
pare § 4, experiment-series 10 and 11). 

Some of the various phenomena Just described may, I 
think, with more justice be designated as specific magnetic 
aftereffect*; but 1 here confine myself to a brief statement f. 
Fii'st, the intensity of the extra currents increases at the frequent 
passage of the current, or at frequent magnetization. This 
phenomenon has already been observed by Herwig ; and he 
has explained it by an increasing mobility of the particles. 
The second of the above Tables shows it very clearly. At 
the same time it follows that the afteraction in consequence 
of the performance of work, which is the subject of that 
Table, does not simultaneously increase ; for the numbers 
Mj are nearly constant, and the difference Wg — '^x sinks from 
1*7, through I'O, 0*9, 0*7, to 0"6. In connexion with this 
is the fact that the resistance of iron generally increases not in- 
considerably on the current being repeatedly conducted through it. 
This phenomenon must not be confounded with that observed 
by Von Quintus Icilius — namely, that the resistance of all 
metals is increased after a single long-continued passage of a 
current through them. The phenomenon is much more pro- 

* I see, ft-cm a memoir by Fromme, just published (Wied. Ann. iv. 
p. 76), that he also uses the same expression tor analogous phenomena. 

t Cunf. Herwig, Stieintz, /. c. , and further, Herwig, Pogg. Ajin. clvi. 
p. 430 (1875). 

Fhil. Mag. S. 5. Vol. 8. Xo. 47. Aug. 1879. M 

150 Dr. F. Auerbacb on the Passage of 

nounccd in iron tlio first time it is used rr;ilvnnically, and 
mostly vanishes after the tenth to the hundredth closin*:;. 
Thus the result with an iron wire (Z= 1()70, fZ = 0-20, H = 2D, 
M=1D) was:— 

Initially ....... ?t' = 7-3501 

After the 10th closing . . 7-3531) 

,, 100th „ . . 7-3552 (const.) 

Loneitudinallv mao;netized . 7-3547 
Magnetized ten times . . 7-3541 
Demagnetized . . . . 7-3559 

These numbers show the afteraction with transverse mag- 
netization by the current as Avell as with longitudinal mag- 
netization. That the decrease of resistance in consequence of 
the latter appears so trifling (it became much greater at equal 
values of H, M, n after the relations of the wire had become 
stationary), evidently depends on this — that the two after- 
actions, as indeed is mostly the case with these phenomena, 
do not go on independently of one another, and therefore, in 
consequence of the accelerated afteraction of the frequently 
repeated transverse magnetizing, a part of the decrease of re- 
sistance is concealed. 

According to the preceding, it appears a probable supposi- 
tion that the permanent alterations of resistance jcith the mag- 
netic state, produced by magnetizing, may also he taken as the 
e.vp7'essio7i of certain jierformances of icork. In fact, on a cur- 
rent passing through an iron wire, constant rotations of the 
molecules will be produced, which at an alteration of the 
arrangement, such as is produced by magnetizing, cannot 
remain unchanged. If these sj^eculations are of a very hy- 
pothetical character, they nevertheless, I think, afford more 
fixed points than those of Beetz. 

Attempts have been made by several to gain new fixed 
points by artificial transverse magnetization of the iron passed 
through by the current. I have not hitherto pursued this 
idea experimentally, — first, because Ave have not, as might be 
inferred from the hypotheses tacitly assumed by the authors 
in question, simply transverse opposed to longitudinal mag- 
netization, but much rather here again, according to the ar- 
rangement, many different kinds of magnetization are conceiv- 
able (wherefore I have, for the sake of definiteness, designated 
the one here discussed as circular magyietization); and, next, 
because these experiments require still greater delicacy of 
measurement than experiments with longitudinal magnetiza- 
tion. The theory requires that artificial circular magnetizing 
(that is, additional to that produced by the principal current), 

the Galvamc Current tlirougli Iron. 151 

if it alter the resistance at all, shall augment or diminish it 
according as the direction of the artificial is the same as or 
opposite to that of the natural circular magnetization, and 
according to their intensities. I am not aware of any expe- 
riment on this point. On the other hand, Sir W. Thomson * 
conducted the current through a square iron plate in a direc- 
tion inclined to the direction of the magnetization. The poles 
of the electromagnet were situated at two opposite sides of the 
square, the electrodes of the principal current in two op^^o- 
site angles. Of the individual current-threads into which the 
plate under these circumstances divides, Thomson investigated 
the two meeting at the margin, each of which consists of two 
consecutive edges, ABC and ADC (fig. 4). The result of the 
experiment was, that the magnetization of the level-line D B 
was shifted into the position De, and consequently the resist- 
ance along A B was less than that along A D, and the resist- 
ance along D C was less than that along B C. Beetz and 
others have pointed out that even the mechanical pull con- 
nected with the magnetizing would hy itself alone have neces- 
sitated this result. I think I must concur in this explanation; 
I will, however, show that my theory is not inconsistent' with 
Thomson's observation, that, under some circumstances, it 
requires the latter, and that these circumstances were not pre- 
sent in the corresponding experiment made by Beetz f (which 
had a negative result). 

Along the line A B, in Thomson's experiment, the directing 
force of the electromagnet will disturb the circular magneti- 
zation more or less, according to its intensity in comparison 
with that of the current-thread, and change it into a trans- 
verse magnetizing, in which all the molecular north poles 
point to the same side of the space. At the same time the 
resistance in certain lines of the current-thread, namely in 
those in which both the magnetizing forces have the same 
direction or make with one another an angle of 180°, will be 
but slightly changed ; in the rest it will be generally dimi- 
nished. Thus the total resistance will either be lessened or, 
if the electromagnet is powerful, somewhat but not much in- 
creased. But just in this latter case the resistance of the cur- 
rent-thread B C must very considerabl}' increase ; for here 
the electromagnet nullifies the circular magnetizing and pro- 
duces a powerful longitudinal magnetization. From this, it 
is true, nothing can be inferred as to how the total resistance 
of A B C varies ; but just as little can be inferred from Thom- 
son's experiments. It merely follows that the whole or the 
greatest portion of any decrease of the resistance, but only 
* Loc. cit. p. 741. t Loc. cit. p. 206. 


152 Mr. S. T. Preston on the Contlmiance of 

the smallest portion of any increase, must fall upon the part 
A B ; and this we in fact learn from the above consideration. 
That I have therein taken no account of the action of neigh- 
bouring current-threads makes no diti'erence; for the result 
of this action is, for A B exactly as for B C, that the mole- 
cular magnets are brought into a position a little nearer the 
perpendicular to the plane of the plate. 

In Beetz's experiment the iron-wire spiral to be magnetized 
was inside the magnetizing copper spiral, so that the turns of 
the one were parallel to those of the other. Consequently 
the molecules were more or less approximately so placed that 
(supposing the windings horizontal and the current flowing 
in the copper in the direction of motion of the hands of a 
watch) all the north poles pointed downward. The principal 
current, on the other hand, called forth a circular magnetizing; 
therefore in the portions of wire belonging to the front half 
of the iron spiral, although the principal current flowed in the 
direction in Avhich the hands of a watch move, the north poles 
in the anterior semicylinders into wh'ch each portion of the 
wire can be resolved were directed more or less upward, in the 
posterior (inner) downward. Conversely, in the portions of 
wire of the hinder half-spiral, the north poles in the posterior 
(outer) semicylinders were directed upward, and downward 
in the anterior ones. If, then, the magnetizing force of the 
principal current is not very little in comparison with the 
other, half of the current-threads present a stronger resistance 
than before the transverse magnetizing, the other half a weaker 
one ; thus the total resistance remains nearly unaltered. The 
negative result of Beetz's experiment is therefore not sur- 

[To be continued.] 

XIX. On the Possibility of accounting for the Continuance of 
Recurring Changes in the Universe, consistently tcith the 
T'endeney to Teniperature-Equilihrium. By S. Tolver 

THE idea of the ultimate final cessation of all activity and 
life in the universe has been contemplated by many phy- 
sicists with some dissatisfaction, and with the desire, if possible, 
to find some explanation or ])hysical means by which so appa- 
rently purposeless an end is averted, and of avoiding the ne- 
cessity for assuming in past time a violation of physical prin- 
ciples at present recognized to exist. The allied notion of an 
unstable universe whose parts tend to agglomerate together into 
one mass by successively falling together, would certainly, to 
• Communicated by the Author. 


Recurring Changes in the Universe. 153 

say the least, appear to have something incongruous and un- 
natural about it, when regarded from a philosophical point of 
view; and however well grounded this aspect of the case might 
appear, still, from the vastness of the subject and the limited 
range of observation, it remains always conceivable that some 
physical link may have been left out, which affects the final 

As previous attempts to explain the phenomena of nature 
as the result of the action in the past of existing physical prin- 
ciples have been invariably welcomed, I venture to submit the 
following conclusion which has presented itself to me. I will 
commence at once by an illustrative case, noticing the diffi- 
culties as they arise. Let us imagine (for mere sake of illus- 
tration) a cubical envelope, Avhich permits neither change of 
volume nor passage of heat, to enclose a space of diameter 
say 10^*^ times the distance between the Sun and Sirius. 
First, let the matter within this space be at the zero of 
temperature. Second, let all the matter within our enve- 
lope be at such a temperature that it is entirely dissociated 
into discrete molecules*. Between those two extremes there 
is room for any number of mean states in which matter 
might be more or less aggregated or discrete. Might not 
the universe actually be in one of these intermediate states? 
i. e. consisting of portions of matter in various stages of 
aggregation, moving among each other according to the prin- 
ciples of the kinetic theory, but not sufficiently rapidly to 
prevent gravity from producing a certain degree of aggrega- 
tion. It should be scarcely nece. sary to observe that we have 
limited our space merely for the sake of fixing our ideas. All 
we require is gained if, instead of using the impermeable en- 
velope, we surround our cube with infinite space filled with 
matter in a similar condition to that which the cube enclosed. 
There might perhaps be some who wouM find a difficulty at 
first sight in conceiving how two masses in translatory motion 
could collide without gravity making them coalesce and so 
the degree of aggregation continually becoming greater and 
greater. But it is to be noted that, if we imagine the masses 
to collide at such a limiting speed that the velocity with which 

* The discrete molecules ■vroiild of course be in motion, rebounding 
from each other in all directions, according to the principles of the kinetic 
theoiy of gases, and pervading the cubical unit of volume uniformly. 
Obviously we must take into account the neutralization of gravity within 
the cubical unit of volume, by reahzing the space outside the cube filled 
with matter in a similar state to that which the cube encloses. The 
known tendency of the kinetic theory is automatically to produce a similar 
distribution of matter per unit of volume. Gravity acting from one unit 
of volume to another is thus neutralized. 

15-i Mr. S. T. Preston on the Continuance of 

the fragments or scattered parts rewound or glance off exceeds 
the greatest velocity of a])j)roach that gravity could generate 
in them when falling together from an indefinite distance, then 
the degree of aggregation after the collision would he less than 
it was before. Indeed, fixing the imagination upon a single 
cubical element of space containing detached solid masses of 
matter, and enclosed by a rigid envelope [other similar cubical 
elements existing outside — and the masses being figured for the 
instant at rest], it is then quite conceivable that such a velo- 
city might be suddenly given to these detached masses of 
matter that the heat developed at their mutual collisions is 
sufficient to resolve the whole into discrete molecules (or a gas) 
pervading the cubical envelope uniformly, i. e. so that gravity 
is incompetent to produce any degree of aggregation (in the 
form of clusters or nuclei) at all*. Is not a less velocity than 
this conceivable which, when communicated to the masses, 
would still leave them some degree of aggregation, dependent 
on the mean velocity of translatory motion 't which velocity 
(though constant from one unit of volume to another) would 
vary greatly from one mass to another in accordance with the 
principles of the kinetic theory — producing corresponding 
variations in the degree of aggregation from one mass to an- 
other without affecting the mean state (per unit of volume). 

The case is comparable on smaller scale to the minute 
masses (each consisting of a number of molecules aggregated 
about a common centre) forming the compound molecules of 
a gas of high complexity. Here it is a known fact that such 
a velocity of translatory motion (dependent on temperature) 
might bo given to these minute masses (compound molecules) 
composing the gas as to break them up into discrete mole- 
cules. A less velocity than this is conceivable at which a 
small degree of aggregation is possible, and a still less velocity 
Avhere a still oreater deiiree of a o-gre Ration can ensue. Indeed, 
if the constituents be numerous so as to admit of a great va- 
riety of groupings, a very considerable range in the degree of 
aggregation is possible by varying the rates of translatory 
motion (dependent on varying temperatures). It is also a 
recognized fact here that the degree of aggregation by any 
given rate of translatory motion (temperature) refers only to 
the mean state, and not to the state of each of the individual 

* It is evident that since we are not limited as to velocity, a certain 
(adequate) velocity must exist, correspoudinjir to an adequate degree of 
energy, thnt would sullice lo produce this nssult. 01" course the cubical 
envelopes are merely used for facility of illustration, and may be supposed 
abolished, substituting for them infinite space containing matter in a 
similar state. 

Recurring Clianges in the Universe. 155 

masses ; for frequently one of the minute masses (molecular 
clusters) may acquire such a velocity in the accidents of colli- 
sion as to break it up into discrete molecules at an encounter, 
these discrete molecules grouping together again in another 
part of the gas, the mean state of aggregation (per unit of 
volume) remaining unchanged. Of course it is obvious that 
there are differences of detail in considering the case of the 
masses of the universe. For exam2:»le, in a compound gas, 
where the central agency producing aggregation is " chemical 
action," the fluctuation in size of a mass (molecular cluster) 
unde]- the collisions is limited, whereas in the case of the masses 
of the universe, where the central agency producing aggre- 
gation is mainly " gravific action " *, the fluctuation in size 

* The agency producing aggi-egation may even be found (when recog- 
nized) to be of the same kind in all cases ("gravific action," "chemical 
action," &c.)- In former papers published in the Philosophical Magazine 
( 8ept. and Nov. 1877, and Feb. 1878), I have called attention to the fact 
that, if the kinetic theory be appplied to the motion of the particles of 
tether [in addition to that of the stellar masses suggested here], the gravi- 
tation of the molecules of gross matter may be accounted for under the 
ingonious fundamental idea contained in Le Sage's well-kno^'u theory, 
•with the removal of all his postulates ; or gravitation maybe shown to be 
the necessary consequence of the mere immersion of the universe in finely 
subdivided matter moving automatically according to the principles of 
the kinetic theory. By the application of thistheo^-y to the stellar masses, 
molecides of gross matter, and particles of fetlier, as a va-st whole, consist- 
ing of matter of different dimensions moving under its own dynamics, a 
grand dynamical generalization would evidently seem to suggest itself. 
It may be noted that, if we reject the now practically defunct conception 
of "force"' in the sense of an "action at a distance" (without the inter- 
vention of matter), no other than a dynamical view of the imiverse is in 
principle conceivable. 

Another consideration woidd seem to have an important bearing on this 
subject. The parts of the molecules of matter are known to possess a con- 
siderable capacity for motion. When, for example, the molecules of a 
gas are exposed to the pulsatory movement of the waves of heat (from 
some radiant source), the parts of the molecules are thrown into motion 
(vibration) ; and this development of motion in the pai-ts is found to pro- 
duce an accession of Irauslatory motion in the molecides as wholes. This 
principle holds independently of scale; and thus it appears that the deve- 
lopment of motion (by any means) in the constituent parts of a mass tends 
(under certain conditions) to produce translatoiy motion in the mass as a 
whole. If the sether, in which gross matter is immersed, be itself in a 
state of internal motion, this motion must inevitably communicate itself 
Cto a certain extent) to the constituent parts of masses of matter immersed 
in the aether, and, accordingly, serve as a supplementary means to the 
development of translatory motion in the masses as wholes. 
•( ' We raa.y observe that, under the kinetic theory of gravity (based upon 
Le Sage's fundamental idea), both the range and intensity of gravity have 
a limit. The range (limited by the length of path of the particles') need 
not be necessarily much greater than that of which we have proof by ob- 
servation, which is but a relatively small range compared with the stellar 
distances. The intensity of gTavity therefore (for this reason) woidd not 

156 Mr. S. T. rroston on the Continuance of 

would not bo thus definitely limited. We are, however, deal- 
ing here with a fundamental matter of principle, not with sub- 
sidiary details*. It appears ditiicult to see where we are to limit 
the scale in the a]>plication of a principle, or how, if the ki- 
netic theory be applicable to the case of a compound oas con- 
sisting of small masses (molecular clusters) of, say, as many i\s 
50 to GO molecules a^iireijated about a connnon centre, it should 
not a|)ply when the munher of molecules aggregated about a 
centre is increased (so as to form a visible mass). It might 
be said that the cases are different, inasmuch as the compound 
molecules of a gas rebound from each other as elastic bodies, 
whereas in the case of the masses of the universe they would 
generally be broken up and scattered at the encounters. This 
objection could only arise, howe^■er, from a superficial view of 
the case. For it is a known fact that the compound molecules 
of a gas often acquire in the accidents of collisions very great 
velocities, and they are thus broken up and their parts scat- 
tered at their encounters. There is, however, on the whole no 
work done (or loss of energy) in this breaking-up of the mi- 
nute masses (compound molecules) of the gas ; for the disso- 
ciated molecules unite again in another region of the gas: and 
SO long as the mean state of aggregation (per unit of volume) 
in the gas remains unchanged, there is on the whole no work 
done. So in the case of the universe, if the mean state of ag- 
gregation remain the same, there would be on the whole no 
work performed by the occasional breaking-up of matter. 
But it may be said that at every such collision of two masses 
of the universe there would be a dissipation of energ}- in the 
aether attendant on the heat developed at the encounter, and 
this energy would be unavoidably lost. But if we regard the 
matter of the universe as (in the mean) uniformly dili'used, as 
it Avould necessarily be under the kinetic theory, there would 
be no such actual loss of energy — merely a radiation back- 
wards and forwards from one region to another. Thus in the 
smaller scale case of a gas, there is undoubtedly a dissipation 
of energy in the aether at every encounter of the small-scale 
masses (molecular clusters) in translatory motion ; but this 
energy is (as is known) not lost, but only radiated to another 

go on iDcreasing indefinitely by the imaginai-y continual piling-up of mat- 
ter, but would attain a tiual maximum. ^\'e allude to this last point as a 
possible detail of interest, without thereby implying that it essentiidly 
aU'ects the main principle we have been developing in this paper. 

* We merely apply in principle the same general mechanical considera- 
tions to molecules aggregated into clusters (lumps) under chemical action, 
as to molecules aggregated into lumps mider gi'avitic action (stellai* 

Recurring Changes in the Universe. 157 

region of the gas, the mean temperature {per unit of vohane) of 
the gas remaiuing the same. One known consequence of the 
kinetic theory is that vast fluctuations of temperature may 
occur in the gas, from one of the portions of matter (consisting 
of one molecule or several) that moves as a whole in the mo- 
tion of translation, to another portion, though the whole 
(I'eckoned by units of volume) may he in equilibrium of tem- 
perature. The same would apply in principle to the case of 
the universe, consisting of portions of matter in translatory 
motion among each other, if we do not limit the scale on which 
the principles are applicable ] or it would follow^ that there 
might be vast dilierences of temperature from one portion of 
matter (stellar mass) to another, while the whole {reckoned hy 
units of volume) might be in equilibrium of temperature. In 
order to have an idea, by inspection, of the mean state of tem- 
perature of the universe, we should require to sweep over a 
unit of volume, containing some hundreds of milions of stellar 
masses (dark and bright), in the same way as we do (on 
smaller scale) in examining the state of temperature of a gas ; 
any appreciable volume of which contains some hundreds of 
millions of portions of matter in translatory motion (at difter- 
ent temperatures). 

If it were possible to visualize the individual molecules in 
a compound gas at normal temperature, molecules would be 
observed in various parts glowing at a white or red heat (and 
some in a state of dissociation); and if the state of tempera- 
ture of the whole gas were judged of from these relativelv few 
luminous molecules, the assumption would be that the whole 
gas was at a white heat. So in the case of the universe, if the 
state of temperature of the whole were judged of from the 
perhaps relatively few luminous masses [which of course can 
alone be visible to us], an entirely false impression might be 
conveyed of the real state. 

If therefore the above suggestion as to the possible applica- 
tion of an admitted dynamical principle on a large scale should 
be found valid, it would follow that the universe may already 
be at uniform temperature, in the sense that the limits within 
which there is fluctuation of temperature are indefinitely small 
compared with the collective universe, but that these limits 
are, relatively to a planetary system, very great, and amply 
sufficient to allow continual physical change, adapted to the 
maintenance of life. 

So in an analogous way as regards the state of aggregation 
of the matter of the universe : since, by the application of the 
kinetic theory, this depends on the temperature, it would fol- 
low^ that the mean state of aggregation of the matter (per unit 

158 Mr. S. T. Prestou on the Continuance of 

of volume), like the mean temperature, is tbo same throutrh- 
out — tbouirli indefiiiite -fluctuations of dimensions would occur 
from one mass to another, in harmony with the fluctuations 
of velocity. 

It would further follow from the principle that, molecules of 
different doTisities (molecular wcif^hts) tend forcibly to become 
uniformly diffused, that by an adequate past duration of the 
universe the different kinds of matter must be uniformly dif- 
fused (per unit of volume) by the continued interchange of 
motion, thoufrh considerable fluctuations of mixture within 
ranoes less than a unit of volume would be possible in harmony 
with the kinetic theory. 

It may be observed that in principle, in order to account 
for the continuance of change in the universe, the existence 
of some process of recurvence is absolutely essential. The 
cooled down material of extinct suns nnist in some way bo 
made available for the development of fresh suns or centres of 
heat. For if this were not the fact, there would be a continual 
accunmlation of the material of extinct or useless suns in the 
universe, and ])rocesses of renewal and maintenance of the 
activity of the universe would come to a deadlock in the ab- 
sence of matter to o})erate u[)on. It seems inconceivable how 
this end could be effected under recognized dynamical prin- 
ciples, excepting through an exchange of motion going on 
among the matter of the universe, involving collisions and an 
alternating renewal and loss of heat : or this seems on broad 
principle the only conceivable way in Avhich there should be 
recurrence, under the condition that the (<(nne matter eliould be 
bisect again. There would appear to be a sim})le grandeur (not 
out of harmony with the recognized characteristics of nature) 
in this great result being brought about by the mere move- 
ment of the stellar masses according to the kinetic theory. 
Moreover the kinetic theory has been mathematically j)roved 
(when a large number of masses are concerned) to produce a 
system of order and synnnetry (or mean similarity of the con- 
ditions in all parts of the system) which is rigidly and auto- 
matically maintained by a process of self-correction under 
dynamical princi})les — a self-acting adjustment of the motions 
continually taking ])lace, whereby a system of harmony and 
order is maintained everywhere, a perfect state of mobile equi- 
librium existing in all parts. 

Those who are inclined to view the physical causation of 
the past in the light of the physical causation of the present, 
or who look upon the princi[»le of the conservation of energy 
as a truth as necessary in the past as in the present (or who 
are disposed to regard ])hysical truths as independent of time), 

Recurring Changes in the Universe. 159 

are bound to believe that some process of recurrence must 
exist, whereby useful change and activity are continued in the 
universe, and the purposeless end of a changeless chaos pre- 
vented — and that we should seek for the explanation of this, 
not so much with the view to prove the fact thereby, but 
rather as a satisfaction or confirmatiou of a fact we already 
had logical o-rounds for believino- to exist. 

That recurring changes exist in the universe seems to have 
been the conviction of Sir W. Grove. He remarks relative to 
this subject (' Corr. of Physical Forces/ page 67): — "En- 
larged observation may prove that phenomena seeming to 
tend in one direction will turn out to be recurrent, though 
never absolutely identical in their recurrence ; that there is 
throughout the universe gradual change, but no finality; .... 
that no star or planet could at any time be said to be created 
or destroyed, or to be in a state of absolute stability, but that 
some may be increasing, others dwindling away, and so 
throughout the universe, in the past as in the future." 

Humboldt also says, as regards this point (Prefice to 
'Cosmos''): — "I would therefore venture to hope that an 
attempt to delineate nature in all its vivid animation and ex- 
alted grandeur, and to trace the stable amid the vacillating 
ever-recurring alternation of physical metamorphoses, will not 
be wholly disregarded at a future age." 

It has been pointed out by Dr. James Croll, in a paper 
published in the Quarterly Journal of Science for July 1877, 
that Helmholtz's gravitation theory of the origin of the sun's 
heat is not alone gufficient to account for a past duration of 
the sun^s heat in harmony with geological evidence as to the 
age of the earth. It is of course evident that all the geolo- 
gical history of the earth must be comprised within the limit 
of the age of the sun. In this paper elaborate geological e^a- 
dence is given tending to prove conclusively that as a limit, 
the age of the earth must be very much (at least three times) 
greater than the time the store of heat could have existed in 
the sun, if the origin of this heat were solely gravitation. For 
it is a known fact- (based upon direct experimental evidence 
of the loss of solar heat by radiation) that the store of heat, if 
it had resulted from gravitation alone, would only have sufficed 
for about 20,000,000 years. Dr. Croll remarks regarding 
this point (page ol7): — " We have not sufficient data to de- 
termine how many years have elapsed since life began on the 
globe, for we do not know the total amount of rock removed 
by denudation ; but we have data perfectly sufficient to show 

that it began far more than twice 20 million years ago 

Now in proving that the antiquity of our habitable globe must 

160 Mr. S. T. Preston 07i the Continuance of 

l)c far prroater than 20 or 30 inilHon years, we prove tliat 
there must liave been .some otber source in addition to gravity 
from which the sun derived his store of energy." Tlie colli- 
sion of matter in translatory motion is then suggested as the 
only conceivable other source of the store of heat-energy in 
the sun — this suggestion having already been made by the 
same author in a ]trevious paper ])ublished in tlie Philosophi- 
cal Magazine for May 18G8, where it is remarked (p. o73): — 
*' The Dynamical Theory of Heat affords an easy explanation 
of at least hoio such an amount of energy Jtiai/ have been com- 
municated. Two bodies, each one half the mass of the sun, 
moving directly towards each other with a velocity of 476 
miles per second, would by their concussion generate in a 
sinqle moment 50,000,000 years' heat^^ [/. e. an amount of 
heat which would cover the present rate of the sun's radiation 
for a period of 50,000,000 years]. 

It would seem to be scarcely realized what a field for rapi- 
dity of motion combined with all the stability or permanence 
of apparent rest the universe presents. It is a mere question 
of scale for bodies to possess any velocities (no consequence 
how great), and yet not alter their relative positions appreci- 
ably in a given epoch of time. Thus a stellar mass, for ex- 
ample, that moved transversely to the observer a distance 
equal to its own diameter [say a million miles, which is roughly 
the sun's diameter] in a second, would appear to the eye to be 
at rest; for the disk of the stellar mass has no apparent dia- 
meter even in the best telescope, and therefore the distance 
moved in a second would be invisible. Yet the velocity of 
the stellar mass in that case would be about five times that of 
light*. Dr. Croll has pointed out (Phil. Mag. July 1878) that 

* Since light requires a quarter of an hour to traverse the diameter of 
the earth's orbit, and since that diameter (182,000,000 miles) would be a 
point when viewed at the distance of the nearest star, it follows that, if 
the nearest star were moving transversely to the observer with the velo- 
city of light, the star might be watched for a quarter of an hour without 
appearing to deviate from its position. The actual angular distance tra- 
versed by the star, after the motion equal to that of light had been going 
on for a quarter of an hour, would be the thickness of a human hair held 
at 25 feet from the eye [this being the known representation of an angle 
of 2 seconds, which is that subtended by the earth's orbit at the distance 
of the nearest star]. This star might move with the velocity of light for 
7| hours without traversing a greater angular distance than the thick- 
ness of a hair held 10 inches from the eye. 

The tendency of modern science is unquestionably to look to a dyna- 
mical interpretation of phenomena in place of the old vaguclir conceived 
statical ideas. The old tendency has been rather in the direction of igno- 
ring the motions of the stellar masses, and of banishing from the concep- 
tions (in the attempt to arrive at some notion of stability in the imiverse) 
all idea of a dii-ect interference or mutual action of the moving parts of the 

Recurring Changes in the Universe. 161 

a star 1000 times more remote than a. Centauri, though moving 
transversely to the observer at the rate of 100 miles per second, 
would take upwards of 30 years to change its position as much 
as V — in fact, that we should have to watch the st..r for a 
generation or two before we could be certain whether it was 
changing its position or not. It is evident that in regard to 
the motions of the stellar masses, some attempt muit be made 
to realize their dimensions in order to have a just appreciation 
of the case. A motion that might seem harmonious and even 
slow in the case of a great ship (for examp e) would be utterly 
discordant and unfitting in the case of a child's toy boat. A 
stellar mass that moved through a fractional thousandth part 
of its own diameter in a second might be regarded as having 
a majestically slow motion ; and yet if its diameter were a 
million miles [which may possibly be an average value], it 
would have traversed a thousand miles in that brief interval of 
time. These considerat"ons may serve to show that if we 
apply the kinetic theoiy to the motions of the stellar masses, 
how completely different the case is from an ordinary gas as 
regards sequence of changes. The molecules of a gas, so far 
from merely traversing a space comparable to their own diame- 
ters in a second, are known as an actual fact to traverse a space 
equal to countless millions of times their own mean distance 
in a second [making roughly about ten thousand million col- 
lisions a second] ; and yet, in spite of this rapid sequence of 
changes, the molecules, as regards absolute velocity, are almost 
at rest compared with the stellar masses. The scale is so incom- 
parably different in the two cases*. Nevertheless, from the fact 
that the energy (heat) developed at the collisions depends on the 
absolute velocity, and of course not on the relative change of po- 
sition of the masses, it becomes thereby possible by a sufficient 
scale to have an absolute velocity of any value however high, 
adequate to an enormous development of heat and explosive 
rebound f at the encounters, combined with so small a relative 
motion (or i-elative change of position) that the masses appear 

universe upon eacli other. We, on the other hand, are led to take the 
diametrically opposite view, and to look to the dynamical actirn of the 
moving parts of the imiverse upon each other as the sole means of ensuring 

• While in the case of a gas the scale is too small for us to overlook 
directly the changes taking place in a unit of volume, in the case of the 
universe the scale is too big. 

t The reboimd vrould be far more than " explosive " in the ordinaiy 
sense of that term, since the expansive action of the heat developed by 
collisions even at moderate planetary velocities (calculably) far outrivals 
both in energy and suddenness the case of explosives. Indeed, if the col- 
liding masses were formed of gunpowder, its ignition at the collision 
would add but little to the explosive energy of the recoil. 

1(12 On the Continiianoe of liecurriiKj Chanijes in the Universe. 

to the eye to be at rest. If it takes so loner for the stellar masses 
to change their mean distances, what must it 1)0 in refjard to tlio 
time taken to traverse their mean length ot" ])ath (previous to 
the encounters); and thus in each individual case an almost 
limitless epoch of time is rendered possible for the conditions 
of life, while in the collective universe that stability and per- 
manence are ensured which can alone rest upon recurring 

In regard to a possible objection that, as far as oV)servation 
lias gone, the proper motion of the stars has not been found 
to exceed 30 to 50 miles per second, it may be replied that 
those stars whose proper motions it has been possible to esti- 
mate roughly, constitute an insignificant and almost vanishing 
minority compared with the rest of the visible stars, which are 
known to be situated at immeasurable distances. It lias l)een 
pointed out by Dr. Croll that it would be scarcely reasona})le 
to expect liDiiinous stars to possess a high proper motion, since 
precisely they would have lost a greater jiart of their ])roper 
motion in the collisions which developed the heat which ren- 
dered them luminous, the j^roper motion having been lost by 
conversion into heat. Mr. Johnstone Stoney, in a paper pub- 
lished iu the Proceedings of the Royal Society for 1868-09, 
has also dealt with the eventuality of collisions among the stars 
in a state of proper motion, and remarks (page 53 j: — " If what 
I here venture as a surmise with resyicct to the proximate cause 
of stellar heat and the origin of double stars is Avhat really took 
place, we must couclude the sky to be peopled with countless 
hosts of dark bodies, so numerous that those which have met 
Avith such collisions as to render them now visibly incandes- 
cent must be in comparison few indeed"*. 

The occasional appearance or blazing forth of '' new stars,^^ 
so notorious in astronomy, as if due to some sudden convulsion, 
would be in harmony with the view of collisions. That the stel- 
lar masses are iu translatory motion, moving among each other 
in various directions and (in general) at such distances apart 
that gravity [if it exists at all at such distances] is incompe- 
tent to prevent the paths from being (sensibly) straight lines, 
is a well-established fact of observation. The application of 
the principles of the kinetic theory to the case would, there- 
fore, seem to su^cest itself rather in the light of a natural de- 

* The fact of the present writer havinir .arrived at the general concln- 
f>ioii3 enunciated in this artich^, before he had seen the papers of Dr. ('roll 
and Mr. Jolinstone Stonev, 9«>rved rather to increase liis confidence in the 
view he had adopted, and which he now ventures to suggest to the i-eadera 
of the Philosophical Magazine. 

On the Theory of Fault >< in Cables. 1G3 

dnction than as a mere speculation. And even independently 
of all other considerations, it would seem more reasonable to 
look to a dynamical interpretation of the motions of the stellar 
masses, than to i-egard them as drifting indiscriminately among 
each other with the absence of all recognized purpose. 
Loudon, June 1879. 

XX. On the Theory of Faults in Cables. 
By Oliver Heayiside. 
[Concluded JBt-om p. 74.] 
1(). npHERE is no difficulty in finding formula? from the 
J- preceding results which will correspond to any par- 
ticular example considered. Such formula, however, have, 
save to the mathematically curious, little value or interest 
unless they are interpreted numerically. Even then the labour 
involved is, save in special cases, out of proportion to the de- 
rived benefit. I shall confine myself to the simple cases of 
direct working without condensers, and with condensers, with 
a single fault in the centre of the line. 

Suppose the signalling is made by means of a batter}' at P 
and 'a receiving instrument at Q, both of negligible resistance, 
and to earth direct. Then 

= nil = m2 = n^ = n^. 
Let there be a single fault of resistance c/i7 at the centre of 
the line. Then 

ianb = 0, 

sm a-\ sni" -c = 0, 

za 2 

by (10) and (11). The latter splits up into 

a a 

sin^ = and tan-=— 2c<7. . . . (21) 

Therefore, when i is even, <7i = ?7r; and when i is odd, o,- lies 

between i-rr and (/ + l)7r. The denominator of (19) is 

, . a 

sm - 

./>(., b) = Jjsin'^ '-^ .Z.r +1 { sin «-^ + "T^sin a(f - 1) } 'd.c 
_ / /-. sin a\ 

Therefore, by (20), 

A 2E 

a' — sm (7,- 

164 Mr. 0. Heaviside on the 

Hence the potential v at time t after the electromotive force 
E which produced the initial state is removed is, from .i" = 

to .r= -> 

2 . n.v 

v = 2EX ~€~''^r; .... (22i 

a— sin a ^ ^ 

and from .i'= — to .v = l, 

. ax 

. a . (X 1\ 

= 2ES r— e~ T- +2ES 

a — sni rt za a — sin a 

which may be transformed into 

— cos ITT 

t; = 2ES ^"""' sin'-^e-'T- .... (23) 
a — sin a I ^ ^ 

(where ./ = /— .r) by making use of (21). 
Let r be the current at Q. Then 

„ 2E ^ —cos ITT -^ 

kl ^ sin a 

If Tq is the initial current, 





r l + 4z_.— cosiV -^ ,,,^ 

from which the arrival curve of the current may be calculated ; 


for 1 — YT is the proportion of the final current received at Q at 

time t after contact has been made with the battery at P. 

17. The most easily calculated cases are r=co and ^=0. 
When r = X), there is no fault, a, = i7r, (22) and (23) both 

2E21 . m.r _!::::i' 
v= — z, —sin —j— e T 
TT I t I 

and (24) becomes 

Y 00 _ '""■-< 

,— = 22 — cos iire • x (25) 

>■ 1 

Theory of Faults in Cables. 165 

This equation (25) corresponds to curve 1, fig. 1 (p. 62), and 
is well known. 

To find the limiting form of the arrival curve when z = 0. 
Bv (23), when z is finite, 

cos ?7r . a.v - 


v = 2Ez ; — sin-^e t 

a — sni a I 

from A-' = to a/ = — . The initial potential Vq between the 
same limits is 

I 1 + 43 

V ? 1 + 4^^ —cos ITT . a./ _— .„^. 

— = — —- — 2 -. — sm-^e 1. . (2G) 

Vq X Iz a — sma i ^ ' 

The (2i— l)th and 2ith terras are 

I l + 4^/^^^~l — ^ T 1 . 2/7ry -<^^]L^\ 

■7-0 — I — = — ^T^sm — ^e T ), 

where a.2i-\ lies between (2« — l)7r and ^iir, and ultimately 
becomes 2i7r when z is indefinitely reduced, so that the last 

expression takes the form -. Evaluating in the usual manner, 

remembering that 




the (2i — l)th and 2ith terms become 

^/ ^iiTx' Uirlt . 2i7rx'\ _(?i![L^' 
-2(cos-j---^sm-j-)e t . 

Consequently (26) becomes, when z = 0, 

V ^%/4:i7rh . 2i'7rx' 2i'7rx'\ -1?!:^ 

— = 22,1 -^Tfrsm-^ cos— y— je t . 

Vq 1 \ .<^' i i I / 

V . r 

Now, when a/ is indefinitely reduced, — is the same as ^ ; 
therefore, when x' = 0, 

r '^ r (Uif\H 1 - '^IhL^ 

■ . r.=?{^-2}^ ^ ^2^) 

From (27), cnrA-e 3, fig. l,is calculated. Tlie intermediate 
curve 2, fig, 1, for which z=\, is calculated from equation 
Pidl. Mag. S. 5. Vol. 8. No. 47. Aug. 1870. N 

1<!(5 Mr. 0. HoavisiiU" on tite 

(24). It is nocossarv in iliis instance, to fii'st find tlio odd as 
from the second oijuation (21) and Tables. 

18. Now for workin<T -svith condensers at both ends. Let 

and let ?-i and ?'2 be both very small. At time t after the in- 
troduction of E at P, the potential of the line is 

cos J- ^..^ 

i' = 2Eri2: i — e~"T m) 

from .r = to .v= ., and 

wo^ _„J., 

^ sni a 


cos ITT cos -^ 


T ... 

r = 2EriS ^ -e~T . . . (29) 

from y = to .x''= — , where x' =-1— x. 
The o's are the positive roots of 


sin a— —COS" ;^ =0; (30) 

a a 1 

COS H = O, tan -r = r. — , 
2 ' 2 2~rt 

xrA:/ being the resistance of the fault in the centre. 

The current V arriving at x—l is V-=r.2cl ^: that is, 

*^ (It ' 

^ 2E ^— a- cos ITT -"^ .01 X 

r= T7»V'22 : e r. ... (31) 

A:/ - sm a 

i "T 

When there is no fault, c = co , (7,=?7r, and equations (28) and 

(29) both become 

CO • _fi^n 

r = Er, + 2EriScos^e "^ (32) 

Here Er^ is placed outside the S, because ^0=0, and the value 

of -. is \ for (7,, and 1 for the rest. The current leav- 


mg A' = is — nc/— ; or 

r,=o = ^f^^'y2fV-T-; (33) 

TJieory of Faults In Cables. 107 

and the current arriving at .i- = / is 

2E „o° ., . -'— /o^N 

Tx=i= -r^r ^r ^17-1, —i' cos 1716 '^ . . (o4) 

fCl ' 1 

19. To find the limiting forms of the solutions when z = 0. 
In equation (29), when i is odd, ai=i7r; and when i is even, 
including 0, and z finite, a^ lies between iir and (i + l)7r, and 
ultimately becomes (i-fl)7r when z = 0. The 2{th and 
(2i + l)th terms in (2d) are 




1 + 

I ^(^^ (2i-{-l)'7rx' _(Ji±}]^'A 
. ex— cos ' J— e t 

SUl ttgi l 

•• (35) 

This vanishes when z=0, and (29) takes the form 

each representing a pair of terms. Now, when z is infinitely 

«,, = (l-4.~)(2i + l)7r 

by (30). Expanding (35) in powers of z, neglecting squares, 
etc., it becomes 

«-m 1 ( ^' ' CLx! 1 a./ 2at aal'\ _"!' 

ziiiv'ic . 4rt < -7- sm ^ cos -y- + -7p- cos -1- 5- e t . 

(^/ La I 1 tj 

where a stands for (2t + l)7r. The same result is reached by 
finding the limiting ratio of the expression (35) to z when 
^2e = {2i + l)7r, making 

1 . a 

C = X- cot rr, 

2a 2 
and multiplying the result by z. Hence (29) finally becomes 

v = 2ErizX < -J- sm 7- + ( -q^ 4 ) cos -^ I e 'r , (36) 

where o,= (21 + l)7r. 

The potential v.2 of the receiving condenser is 

r2 = 16E?v-24 ^ m^ -,\e t ;. . . (3^ 

and the current V entering the receiving condenser is 

_(2i + l)27r2; 

P 16E 

i7V~:^| - ^ j^ + ^ (2^ + 1)V I e T . (3b) 

Curve 3, fig. 2, is calculated from (37), and curve 3, fig. 3, 
from (38); curve 2, fig. 2, from (29), making 0/ — i) -, and 


168 Mr. 0. Heaviside on the 

curve 2, fifr. 3, from (31). In the last two 2 = |, and the even 
as arc found by Tables. 

20. The two important solutions 

, = E(l-^)— e X , . . (39) 


r = Eri + 2Eri2cos^e t", .... (40) 

whore, in (39), v is the potential at .rat time t after the intro- 
duction of E at .v = 0, both ends being to earth, and in (40) 
V is the same when condensers of very small capacities i\ii and 
Ticl are interposed at the ends, there being no foult, may be 
Loth deduced from the corresponding formula when the con- 
densers are of finite ca})acity. Suppose initially the conden- 
ser at .i- = to be charged to potential E, and the potentiyl of 
the line and the condenser at x = l to be zero, Avith no im- 
pressed electromotive force in the system. Then at time t the 
solution is 

^ . . fax ,\ -'^'i 


and therefore 

tan h= , tan (a + M = 


•i?'2a'^ — 1' 

^^"«= .. .. ^2 1 (41) 

A = 

E?'Jcos?> , f'^ . fax ,\ , , ^ r^lcosCa + h) 

— i hi X sm I ^ + ?> \dx + X ^ ^ 

r\a Jo V I I ^'2^ 

cos'- 6 r' . 2A''*'' I 7\ 7 ,cos-(rf + /') 




The result is 

. ax ax 

i\a sm ~j cos -j 

v= T^^J 2E2 , — e' T-, (42) 

r, ' ^\ 1 + r^av 

where the constant term arises from the zero root of (41). 
Now, when ?-i = /'2 = 0, the other + roots of (41) are tt, 27r, 
37r, . . . ; and (42) then becomes the same as (40). But when 
7'^ = 7'2 = X), the roots are the same with the addition of a se- 
cond zero root. In the general term of (42) make 

1 + cos a 

Theory of Faults in Cables. 169 

which follo^ys from (41) ; and find the limit when a = 0. The 
result is 



This, added to ■^, what the constant term in (42) becomes 
when Vi = r2=^ , makes 



which is the constant term in (39), The remainder of (39) is 
immediate! J deducible from (42) by making ri = ?"2=^ • 

21. The solution (40) for the potential in condenser work- 
ing could be deduced from that for the current in working with- 
out condensers. For, in the latter case, the final result of the 
introduction of an electromotive force at .t-=0 is a current in 
the line of the same strength everywhere, and i- = at .v = 
and cV = I : and in the former the final result is that the po- 
tential of the line is the same everywhere, and y-. = at a'=0 

and a;=l. Both the current and the potential must satisfy 
the same partial differential equation. . Hence the current in 
the latter case at .r at time t must rise in the same manner as 
the potential in the former. Now 

y=^Jl + 2Xcos^-e t|. ... (43) 

is the solution for the current in working without condensers, 


where jj is the final uniform current. In the condenser-pro- 

blem the final uniform potential is — j— =Eri, substituting 

which for jj in (43), and changing y into v, equation (40) 

results without a separate investigation. It is also very re- 
markable that (40) and (43) are capable of expression in an 
entirely different form, leading to the identity 

2V^/1 -us "l-nx , -1!l2 47r^ , -?!f Gtta' . 

= - I X- -f e «- cos h 6 «^ cos he "^ cos + . . 

a \2 a a a 

well known to mathematicians. 

When i = 0, the current as given by (43) is zero every- 
where, except at a' = 0, where it is infinite; and in (40) the 
potential is zero every where when ^ = 0, except at ^ = 0, where 
it is infinite. These impossible infinite values arise from the 

170 Mr. 0. Hca"\nside on the 

nefjloct of the battcrv-resistance in the one, and the conden- 
ser's capacity in the other instance. All mathcniatical inves- 
tigations of physical questions are approximative ; and being 
such, impossible results arise in extreme cases. If R is the 
battery-resistance, the current at .'c=0 Avhen t = cannot be 

greater than j^ ; but since there is always self-induction, the 

currentj when ^ = 0, is mathematically zero, rising in an ex- 

tremely short time to ^, and then falling to its final strength. 

The actual rise of the ciirrent is more complex, on account of 
electromagnetic oscillations. Thus, from infinity we have got 
dovni to zero for the current at .r = when f = 0. 

22. When we introduce the coefficient ^^ = ^t— m, calcula- 
tions become complicated by the ])resence of imaginary roots. 
That there must be imaginary terms in the solutions will be 
evident when it is considered that electromagnetic induction 
imparts inertia to the electric current, thus causing oscillations, 
and that 

., , . /'ax , \ - "3. 

cannot contain oscillatory tenns with real values of a. When 
there is a pair of terms in which A, <?, and h are imaginary, their 
addition causes the elimination of the imaginary parts, and the 
result is real, as indeed it must be if the problem has })hysical 
reality. It is also evident that if in a physically real problem we 
we have a single imaginary root, it must be of the form 
a=0±n "^Z— 1, which makes cr real. 

Taking a simple example, let the line be to earth direct at 
A"=0, and to earth through a coil of resistance mid and electro- 
magnetic capacity L at .i"=/. Also let there be initially a 
potential distribution 


in the line, and a current 

through the whole circuit. This stiite would be produced finally 
by E at .r = 0. At x = 0, t- = 0, and at x = /, 

= I- + ml -r + si'' :r^' 

TJieonj of Faults in Cables. 171 

At time t, 

^ . . a.v - "Ji 
r = 2Asiny6 t, 

where the «'s are the + roots, including imaginary roots with 
+ real parts, of 

tan a ., 

= — ??i + sa , 



f . , a.c 

sla' cos""^ a 

/- 6 sni 'la ^ „ \ 

a\\ -z Im cos a J 

For simplicity, put m=0, then 

V 2E . ax -"^ .... 

' = ^- A 3 sin 2aN ^'"T^ ^' • • (") 


tan a 2 / < - a 

a ^ ^ "^ 

When s is large, there is no trouble with imaginary roots. 
There is a root of (45) a little above zero, another a little 

under — ; and the rest are nearly -^, -^, .... Hence, when 

s is large, (45) becomes 


to determine the lowest root, or 

., 1 T.kl 

a'= -= -J — 
s L 

Therefore (44) is nearly the same as 

and the current nearly the same as 

E -'^ 
^=kl' '+••• 

This case corresponds to a short land-line, the self-induction 
of the receiving instrument causing greatly more retardation 
than the electrostatic capacity of the line. The current at 

1 72 Mr. 0. Heaviside on the 

,r = I is always + . At ,i' = it is first — for a xerj sliort time, 
and thorcaflor +• Except at first, tlio current is of the same 
strength throughout the circuit. Of the h'ne's initial charge 

of potential E ( 1 — t)j^ portion of potential E constant every- 

Avhere discharges quickly, nearly as if the line were insulated at 

x = l. The other part of potential j- disappears exactly as 

the current decays, after the first moment. Or, more simply, 
the inertia of the current in the electromagnet causes the cur- 
rent at .r = Z at any time to be stronger than it would have 
been without self-induction, in which case the current would 
be. simply due to the line's charge. This charge, therefore, 
cannot sup])ly enough electricity for the current ; and the line 
becomes negatively charged, first at the end .v = I, and after- 
wards all along. When this has happened the line-current is 
constant everywhere, and the — charge and + current die 
away uniformly. 

As s decreases, the two roots of (45) lying between and 


^ approach eacli other. When s reaches 1*47, they both 

become =1*1306, and simultaneously 

3 sin 2a 

1 = 


so that in the solution (44) the first term becomes —a? , the 
second + oo , their sum remaining finite. As iS sinks below 
1*47, the pair of roots become imaginary, and the first two 
terms of (44) may be put in a rather complicated mixed real 
form, indicating oscillations. When s reaches zero, the cable 
discharges in the ordinary "svay. 

From (44) it follows that the potential at time t after intro- 
ducing an electromotive foi'ce E at a' = is 

r = E(l-7 -:S ., ■ . ^ sm-y-e t., . (46) 

\ 2a J 

The electromagnet is here at a=l. Suppose now it is trans- 
ferred to .i'=0, other things being the same ; then instead of 
(46) we shall have 

-f^/^ .r\ ^ 2E cos a . /^ x\ -1-J. ,,^ 

"V — I^) 

Except when .<t = 0, the permanent state of charge is arrived 
at in an entirely ditfereut manner in the two cases, v in (46) 

Theory of Faults in Cables. 173 

is generally greater than v in (47) at any time. In the ex- 
treme, when s is large, the potential of the line according to 
(46) becomes nearly E everywhere, and afterwards settles 

down to E(l— yV thus. 



whereas according to (47) it rises, thus, 

/ .J.N ilt 

,. = e(1--J(1-6-l) + ... 

In spite, however, of this great difference in the phenomena 
of the charge, the current at x = l rises in precisely the same 
manner in both instances, as will be seen on differentiating (46) 
and (47), and making .i' = /. 

23. In the following example we have to deal AWth a single 

imaginary root. Suppose the line is initially charged to po- 

tential -^, that the end x = is to earth, and that the current 

entering the cable at .i' = / after ^ = Ois simply proportional to 
the potential there at any moment. That is, i' = at .i'=0, 

and v = ml ^- at x=L where m is a + constant. At time t 

the solution is 

^ 2E(/n^l)cosflr . a.v -"21 .,^,^ 

a{l — m cos- a) I ^ "^ 


tan a = ma. 
There is one particular case where the potential remains un- 
changed, viz. when m = l . All terms in the expression for r in 
(48) vanish except the first, for which a = 0. The limiting 
value of gj, 

2E(sina — a cos a)sin-j- 
sm^;=. * 

^ a(a — I sin 2a) 

when a = is -j-; so that (48) is simply 


when m=l. If m is greater than 1, v ultimately vanishes ; but 
if m is less than 1, an imaginary- root a = n s/— 1, where n is the 
+ root of 

e" — g— " 

~ir~. » =;««, 

174 Mr. 0. Hoavij>ide on the 

comes into operation. The first term of (48) then increases 
with t without limit, tlie rest ultimately vanishing. 

24. In general, the conditions imposed at the ends of a 
cable, when there are no impressed electromotive forces, are 
of the following form : — 

At .1-=/, 

0=v + u/^+n,A + (50) 

Here mi, . . . , //j, . . . , are constant^!, and r is the potential at 
any time. 

Supposing there are no intermediate conditions, there is a 
single solution of the form 

r=SAsin fc +?>je~ T, .... (51) 

pro^^ded that the right-hand side of (51) can l)e made to 
satisfy (49) and (50), and to equal /(.?■), an arbitrary function 
of .1- when t = 0. 

It follows from (49) and (50) that 

tanA= Vr ^ , . . (52) 

i — ?/<2« + m^a — ... 

tou(a + ^)=-^f=^ f + "'f---- ;. . . (53) 

and from these tan a can be expressed similarly, say 

tan<^=--^^ — 3^^_^__ ^ ^ ^ ^^4^ 

and the a's required are the + roots, real and imaginary, of 
this equation. 

?/ = V I sni ( -y- + 1^1 j sm ( -y + b^ULv, 

Avhere a^, I'l^.a^, h are any two pairs of values of a and f>. 
Then, by integration, 

rtiflg / 7 \ / 7 \ f tan(ai+/>i) tan (02 + ^'2) 

Uj — O^ I, Oi <72 

«i«2 7 7 (tiinbi tan 62") .-.. 

7j , cos hi cos Oo < > . . (55) 

«I — "2 ' i ('1 "2 J 

S^ubstiinting in (.i5) the values of tan(" + ^') and tan ^ from 

Thewy of Faults in Cables. 175 

(53) and (52), the bracketed quantities are always divisible 
by a^^—a\, and ?; is expressible as 

n = ri0i(oi, hi)j>i{a-2, h) + r.2(f).2(ai, ?>i)<^2(«2, h) + . . . ; (50) 
?*. €. in the form of the sum of a number of products, each 
being a function of a^ and hi multiplied by the same function 
of 02 and h.2 and by a constant r. 

Then assuming 

El = 2A<^i(a, h), Eo = SA(/)2(«, h)..., 
it follows that 

1 C^ /a V \ 

J \ /(.r) sin ( ^ +^; ) f/.v-?'iEi<^i(a, ?/)-?'2E2</)2(o. l>)-. . . 

A=i^l^^ 11 I (57) 

I ^ sin^ (j + b'^ dx-r, \Ua, Z.) p- r,_ {</.,(«, b)]' - . . . 

When there are intermediate conditions, producing discon- 
tinuity in V or — &c. at certain points Xi, a\, &c., each sec- 
tion must have its own series of the form (51). The a's are 
the same for every section, being determined by the resultant 
of all the conditions. The A's and Z/'s are different for each 
section. Thus 

/(.r) = SA sin(Y +^) ^^'^^^ ''"^^J *o 'f" = 'f'ij 
= XA'sin/'y +^'] x^ Xi, 

= ^A-sm(^^ + b-) X, 

The intermediate conditions enable A', b', A", b", ... to be 
expressed in terms of A, a, and h. If 

?/= ^ r 'sin^^+Z^Asin/''^' +b2\clx 

then u' may, as before in the case of ?/, be put in the form (50), 
and the value of A follows. 

+ ...-SE;'0((Y,?.) 


+ ...-2;-.;c/>(a,/.)l2 

176 Mr. 0. Heaviside on the 

Tho arbitrary quantities Ei,E2, ... in (57) and (58), or 
rather, as many of them as turn out to be independent, are 
easily found to depend on the initial electromotive forces resi- 
ding in those parts of the system in connexion with the cable, 
either at the ends or intermediate, which influence v at time t 
independently of its value /(.r) when t = 0. 

If, for example, we join two points .t'l and a'2 througli a coil, 
its self-induction will introduce one E ; and if this coil have 
a closed circuit near it, a second independent E will be intro- 

25. Considering the line as of infinite length both ways, it 
will be found that if 

V =:/(.r) = 2A sin (y + Z*) , • • • (59) 

where the a's are determined from 

7*1 a — h M^ + 7ua^' — ... / /.rv s, 

*"""=- l-V^ + A ^^^TTT' • ■ • C'O) 

then will v satisfy the differential equation 

everywhere, thus expressing the relation between the values 
of/(.i-) at any two points separated by a distance 2L Or, 
which is the same thing, 

« = ^-''S.+^-=''S+W'^ + ..., . . (62) 


^1= 1 + 7*1, 

7 1 ^'1 7 r 

^■3=^+ J + ^'2 + ^'^' 

/• - ^ 4-''l4- ''2-J-''3 , 7 ,7 

ii ii '^^ ^ " 

In the particular case 7/i = 0, 7*2 = 0,..., equation (61) 
reduces to 

/Of + Z) =/(.,- 0, (63) 

which sim])ly expresses that /(.r) is periodic, repeating itself 
at intervals 21. 

Starting from this equation, or an equivalent one, Mr. 
O'Kinealy (Phil. Mag. August 1874) proves Fourier's theo- 


Theory of Faults in Cahles. 177 

rem for periodic functions ; that is, solving the linear equation 
(63), its solution is found to be 

/(a;) = 2 A sin ('-^ + A (64) 

Hence it is concluded that an arbitrary function /(.i-) may be 
expanded in such a series as the right-hand side of (64), 
though this proof of the possibility does not tell us how to do 
it. Mr. O'Kinealy, hoAvever, completes the solution in the 
usual way, leading to 

1 r^' 1 {ttvC^^ i-rrv 

/(^) = 21 1 -^^^^ da;+ ^X cos -^ j /{.v) cos —^ dx 

, 1^ . i'TTxC'^'^ y , ."iTTX ,^,. 

+ ^ 2 sm -p ^ ;{x) sm-v-. . {C^o) 

t. • 

Similarly, if we start from equation (61), which is linear, 
with constant coefficients, and includes the above case, we may 
easily prove that its solution is (59), with the condition that 
the a^s therein are the + roots, real and imaginary, of (60), 
the A's and 6's being undetermined. Or Ave may get the 
same result from (Qi), the a's being now found from 

= k^a-k^a^-irh^i^- {<oQ>) 

It will be observed that (60) or (QQ) have numerically equal 
+ and — roots, each pair of which go to a single term of (59). 

Here again the proof, if it may be now called a proof, gives 
us no information as to how to find the coefficients settlino- 
the amplitudes ; and even the phases are undefined without 
further knowledge. But in working out practical problems 
requiring arbitrary functions to satisfy certain conditions 
when expanded in a harmonic series, the physical nature of a 
particular problem will usually suggest, step by step, the ne- 
cessary procedure to render the solution complete, as in the 
last paragraph 24 ; and the completion of a solution is of far 
greater importance than any proof that the solution is possible. 

With respect to the periodic series (65), it is only applicable 
to a cable when the ends are joined so as to make a closed 
circuit, changing 21 into / ; and there must be no external 
electrical connexions with the cable. If there are connexions 
at a point, or at several points, even without interruptin o- the 
continuity of the cable, although the potential of the cable will 
now repeat itself every time x is increased by / or 21 <tc., yet 
the periodic form (65) will obviously not be suitable. The 
proper series are of course more general, and pass into the 
form (65) in Umiting cases. 

[ 17cS ] 

XXI. InteUiijence and Miscellaneous Articles. 



A FTER several unsuccessful attempts, I have at last, on April 1st 
■^^ ami 2nil, obtaiued fairly satisfactory observations of the spec- 
trum of this comet. It consists of three bands, like the spectra of all 
the other comets hitherto observed, the bauds being well defined at 
the lower (least refrangible) edge and fading out towards the upper. 
The spectrum is so faint that observation is very difficult, and I 
was able to determine the position of only one of the bands — that 
in the green, which is much brighter than the other two. 

The instrument employed was the 9 1 -inch refractor of our new 
observatory, armed with a one-prism spectroscope of sufficient dis- 
persive power to separate the D lines clearly : the eyepiece has a 
micrometer which carries a bar thick enough to be seen on the 
backgrouud of even a very feeble spectrum. The observation was 
made by placing the bar so that the bright edge of the baud should 
be just visible as a thin line, the rest of the band being occulted. 
The instrument has also a scale like that of the ordinary chemical 
spectroscope : and the position of the micrometer-bar is determined 
both by the reading of the micrometer-screw and by the reading of 
the scale, illuminated for a moment aft<?r the bar has been set. 

On April 1st I got three scale-readings — respectively 99*9, lOO'O, 
and 100'4, the value of one scale-division in this part of the spec- 

o , 

trum being very nearly 25 units of Angstroms scale, or about 
double the distance between the extreme lines of the h group, the 
readings decreasing with the wave-length. 

Just before dark, ?>, in the spectrum of daylight coincided with 
100 on the scale ; also, immediately aft^r the third pointing and 
without distui'biug the telescope, spectroscope, or micrometer, the 
flame of a Bunsen burner was presented to the slit ; and the lower 
edge of the green band in the well-known spectrum of this flame 
was found to show itself at the edge of the occulting bar precisely 
where the comet- spectrum had been. We may therefore fairly 
conclude that the lower edge of the central band in the comet-spec- 
trum had a wave-length of very nearly 517 millionths of a milli- 
metre. The observation of April 3rd conlirms this, though but a 
single reading could be obtained. The only special interest in this 
observation lies in the fact that in 1868 Mr. lluggins obtained a 
somewhat different result for this same comet. 

In an elaborate paper published some years ago by Yogel in 
Poggeudorff "s Anaalen, upon the spectra of comets, he comes to 
the conclusion that there are several different kinds of cometary 
spectra, the diffei*ences lying merely in the waAC-length of the 
bauds. But he seems to have reached this conclusion by assigning 
rather too high a degree of accui-acy to the observatious. With 
the exception of Brorsen's comet, it would seem that the discre- 
pancies between the different results are entirely within the range 
of probable error, and that there is no valid reason for supposing 

Intelligence and Miscellaneous Articles. 179 

more than a single cometaiy spectrum, slightly modified in different 
comets by differences of pressure and temperature. 

It would now appear from my observations that Brorsen's comet 
also must fall into line with the rest. 

I am entirely at a loss how to explain Mr. Iluggins's result. It 
can hardly be that the comet has really changed its spectrum in 
the meanwhile : and a careful reading of his account (Proc, Roy. 
Soc. vol. xvi. p. 38S) gi\es no light as to how an error could have 
crept into his work ; on the other hand, every precaution would 
seem to have been taken. However this may be, 1 am quite positive 
as to the accuracy of my present result — that the middle band of 
the spectrum of this comet now coincides sensibly (to a one-prism 
spectroscope) with the green band in the hydrocarbon spectrum. 

The comet is moving very nearly in the path assigned by the 
ephemeris of Schulze. It is easily visible in the 3-iuch finder of 
the equatorial, and in the telescope itself appears as a round nebu- 
losity, between 30" and 40" in diameter, without definite nucleus, 
though much brighter in the centre. Before the new moon a faint 
tail was visible, about one half degree in length. It appeared like 
a thin streamer, much narrower than the head of the comet, perfectly 
straight, and directed from the sun. — Silliman's American Journal, 
May 1879. 


It is known that Stokes, in his important researches on fluo- 
rescence, laid it down as a principle that the refrangibility of the 
light emitted by fluorescence is less than that of the exciting ravs. 

Stokes's law has lately been called in question by Lommel, who 
in several memoii's published in the Annalen der Pliysilc has sought 
to show that it is not a general law, and that there are cases in 
Mhich the fluorescent light possesses a greater refrangibility than 
that of the incident light which excites the fluorescence. The 
results obtained b_v Lommel in his experiments have been confirmed 
by B. Brunner (of Prague) and Lubarsch (Berlin) ; but Hagenbach, 
the author of some very accurate studies on fluorescence, was not 
able to arrive at the same results as Lommel. 

After repeating the experiments described in the memoirs of 
these physicists, it appeared to me necessaiy, in order to decide 
this controverted question and give an experimental proof of 
Stokes's law, to discover a method that would permit direct measure- 
ment of the refrangibility of fluorescent light and its comparison 
with that of the incident light exciting the fluorescence. For this 
purpose the light of the exciting rays operated on must be perfectly 
homogeneous. This can be attained by making use of the method 
first employed by Maxwell and Helmholtz, and afterwards by several 
other physicists. The following is the method I have used in 
these researches : — 

The solar rays reflected by a heliostat were concentrated by an 
achromatic lens upon a slit, behind which were placed two flint-glass 

180 Intelligence and Miscellaneous Articles. 

prisms and an achromatic lens ; the latter was separated from the 
slit by twice its focal distance. This araugemeut gave me a spec- 
trum sullicienlly pure for the principal lines to be seen in it. The 
spectrum was expanded on the side ot' a box in which was a 
movable slit, which could be shifted to tlie dill'erent parts o£ 
the spectrum, and the breadth of which could be modilied at plea- 
sure. Through this slit I let certain rays of the spectrum, which 
I previously caused to traverse a Hint-glass prism, enter the box, 
which contains a vessel filled with fluorescent liquid. After this, by 
means of a reflecting prism I direct these perfectly homogeneous 
rays upon the fluorescent liquid. Between the surface of the liquid 
and the slit in the side an achromatic lens is i)laced, which produces 
the coloured image of the slit upon the surface of the fluitl. With 
a second reflecting prism I direct the hght which comes from the 
fluorescent liquid into the slit of the collimator of a Brunuer's 
spectrometer. In the field of vision of the telescope of the spectro- 
meter I get two coloured images — one produced by the fluorescent 
light, the other that which is directly reflected at the surface of the 
fluid. I then measure the minimum deviation of these two images. 
I give the values 1 have obtained for fluoresceine : — 

Incident light. 

Fluorescent light. 

Width of the 

Mean deviation. 

Width of the 

Mean deviation 

2 5i 

50 38 

O ( 

1 25 

48 43 


49 59 


48 18 


49 60 


48 12 


48 18 

1 60 

48 60 


47 56 


47 48 

These experiments show that the fluorescent has a lower refran- 
gibility than the incident light. I have repeated the same experi- 
ments with eosine, naphthaline-red, and chlorophyll, and obtained 
the same results. 

In my researches I have taken the fluids at different degrees of 
concentration, and in layers of different thicknesses ; and the 
result has always been the same. Each fluid has in the spectrum 
certain rays which excite in it the strongest fluorescence ; with 
other rays the fluorescence will be feebler; and it will disappear 
if rays still less refrangible be operated on. All the rays in the 
spectrum which are more refrangible than the fluorescent ones 
excite fluoi-escence in these fluids. It is upon naphthaline-red that 
I have obtained the greatest change of refrangibility of light, iu 
which case the incident rays, whose index of refraction for flint- 
glass is 1-63917, were changed into rays having the refraction- 
index 1-01521. 

After these investigations I think I may conclude that the law 
of change of refrangibility of light is perfectly correct in the 
general form in which it was given by Stokes. — Comjites liemhts de 
V Academic des Sciences, June 9, 1879. 







XXII. Chemical Affinity. By M. M. Pattison Muir, Prcelec- 
tov in Chemistry, Gonville aiul Cains College, Cambridge* . 

IN the yeai' 1780 Bergmann formulated a general theory of 
chemical affinity. The leading points in Bergmann's 
theory were these. The affinity between two bodies is inde- 
pendent of the masses of these bodies which may be brought 
into mutual contact ; under like condition the value of this 
affinity is constant. The relative affinity-values of various 
substances ma-y be empirically represented by the amounts of 
these bodies Avhich mutually combine together : thus, if an 
acid combine with a series of bases to form neutral salts, the 
affinity of the acid is greatest for that base the greatest amount 
of which is taken up by the acid. Conversely, a base has the 
greatest affinity for that acid which combines with it in largest 

In 18Uo BerthoUet published his great work Statique Chi- 
miqne, in which he sought to show that the chemical action 
of one substance upon a second substance is proportional to 
the mass of the first and its affinity for the second. The pro- 
duct of these two quantities is called by BerthoUet the " che- 
mical mass " of the substance. Complete decomposition of 
one compound by another is never brought about, according 
to BerthoUet, by chemical affinity alone ; this force must 
always be aided by what the French chemist called cohesion 
and elasticity. 

Bergmann considered only the affinity of one body for 

* Communicated bv the Author. 
Phil. Mag. S. 5. Vol. 8. No. 18." Sept. 1879. 

i&2 Mr. M. M. Pattison Muir on 

anotli(M"; Borthollot considered also tlie masses of the acting 
bodies and the jdiysical actions which aided the purely che- 
mical changes. A substance with a small affinity for either 
of the constituents of another substance was nevertheless, ac- 
cording to Berthollet, capable of decomposing the other, pro- 
vided the mass of the first substance was large compared with 
that of tlie second. The atiinity of an acid is in this view 
greatest for that base with which it combines in smallest 
quantity, because, if the affinity be large, the mass must be 
small as compared with the mass of another base which has a 
small affinity for the given acid ; otherwise equal amounts of 
chemical work would not be done in forming each of the neu- 
tral salts. 

The theories of Bergmann and Berthollet were antagonistic. 
Since the year 1803 chemists have now inclined to one, 
now to another. Modifications have been made in each; but 
uo new important theory has been advanced. 

The most important contributions made within recent years 
towards the final solution of the problem of chemical affinity 
are contained in two })apers by Guldberg and Waage, and 
tluv^e papers by W. Ostwald. 

The object of this paper is to give an account of the results 
obtained by these naturalists. 

The first paper by the two Christiania Professors was pub- 
lished in 1867, and is entitled " Etudes sur les affinites chi- 
miques ;" the second paper by the same authors appeared in 
the March number of the present year of the Journal fur 
praldische Cliemie. Ostwald's papers, entitled " Volumche- 
inischen Studien," are to be found in Pogg. Ayin. Erganzg. 
Bd. viii. p. 154, and in Jonrn. prakt. Chem. [2] xvi. 385, and 
xviii. 328. 

Guldberg and Waage do not attempt to formulate a general 
theory of chemical action ; they confine themselves to a con- 
sideration of the action of mass in chemical changes. Tlie ex- 
planation which they give of this action is singularly simple, 
and so exact as to allow of matheiuatical deductions being 
made, which are shown to hold good by the results of expe- 
rimental researches. 

Ostwald considers the measurement of affinity as exerted 
between acids and bases in solution combining together to 
form salts- which are soluble under the experimental conditions. 
Berthollet's statement, " Toute substiince qui tend a entrer 
en combinaison, agit en raison de son affinite et de sa quan- 
tite " {Statique Chvnique, p. 2), has been extended and ren- 
dered more exact by the researches of Guldberg and Waage. 
These naturalists have given a definite meaning, independent 

Chemical Ajjinity. 183 

of hypothesis, to the expression " coefficient of affinity." They 
thus express themselves : — 

'■ Let two bodies, A and B, be converted, by double substitu- 
tion, into A! and B', and let A^ and B' be again reconverted, 
under the same conditions, into A and B, neither of those changes 
will be complete. At the close of the reaction there are present 
four bodies A, B, A', and B^; and the force which caused the for- 
mation of A^ and B' is held in equilibrium by the force which 
caused the formation of A and B. The force causing the for- 
mation of A' and B' increases proportionately to the coeffi- 
cient of affinity of the reaction, but is also dependent upon 
the quantities of A and B : we have found that this force is 
proportional to the product of the active masses of A and B. 
If the latter be p and q respectively, and the coefficient of affi- 
nity be k, then the force is represented by 


This expression also evidently represents the amounts of A 
and B transformed in unit time into A' and B'. ... If the 
active masses of A' and B' be // and q' respectively, and the 
affinity-coefficient of the reaction A' + B' = A + B be equal to 
Jc' , then the force which tends to bring about the reformation 
of A and B is 


This force being held in equilibrium by the first, we get the 

kpq = k'p'(^ , 

" By experimentally determining p, q^ pt' , q' , the proportion 
k : ¥ can be calculated; and from this the result of the reac- 
tion for each initial condition can be determined." 

Active mass of a body is defined as the amount of that sub- 
stance in unit volume of the chemical system which undergoes 
change. The coefficient of affinity is dependent upon the che- 
mical nature of A and B and upon the temperature. 

Tlie equation expressing the conditions of equilibrium 
(kpq=ik'p'q')\xo\A?> good only when the action of secondary 
forces, ?". e. forces whose action is to be traced to the pre- 
sence of compounds other than A, B, A', or B^ is overlooked. 

" If the number of molecules of A, B, A', and B' before the 
reaction be represented by P, Q, P', and Q', and if .fbe the 
number of molecules of A and B transformed into A' and B', 
then, supposing the total volume to remain constant during 
the reaction, we have 

184 Mr. M. j\r. Pattison Mnir on 

and by subslitntin;;' tlioso values in ilio equation of e(|uilibrium 
and nuiltij)lyiii<i; by V", we ^et the general equation 

(P-.r)(Q-.f) = |(F + .fXQ' + .^-)-" 

Those reactions which consist of two parts, the direct and 
the reverse chemical chanf^e, are most favourable for the study 
of tlie influence of mass. As examples of this class of changes 
may l)e cited: — the oxidation of a metal by water-gas, and the 
reduction of the metallic oxide so produced by hydrogen; 
the dissociation of a substance A B under conditions such that 
A B and A and B (the products of the dissociation) are simul- 
taneously present in the chemical system ; the division of two 
acids between two bases so as to produce a soluble and an inso- 
luble salt ; and the mutual decomposition of two soluble com- 
pounds with the production of substances themselves soluble 
under the experimental conditions. 

In their earlier paper Guldberg and Waage give the results 
of a long and elaborate series of experiments upon the action 
of carbonates of the alkalis on barium sulphate, and of alkali 
sulphates upon barium carbonate ; they also consider the results 
obtained by Berthelot and St. Giles in their examination of 
the reaction between alcohol and acetic acid, which results in 
the production of acetic ether and AA'ater. From these, and 
other quantitative results, the law of mass-action already stated 
was deduced. 

In their later ])aper the same naturalists detail the results 
of their examination of many difl^erent reactions, and show 
that in each case the law of mass-action holds good. 

Guldberg and Waage recognize two main groups of chemi- 
cal forces : — the true forces of affinity, which bring about the 
formation of new chemical substances; and the secondarij forces, 
the action of which is to be traced to the presence of foreign 
bodies, i. e. bodies other than those directly undergoing che- 
mical change. 

Guldberg and Waage do not think that a comjilete account 
of a chemical change involving simultaneous series of decom- 
positions and recompositions can be given, if regard be paid 
merely to the forces of attraction at work between the sub- 
stances, or the constituents of the substances, upon which the 
change is effected ; they deem it necessary to consider the mo- 
lecular and atomic movements of these substances. 

The equililirium attained by a system in which the changes 

A + B = A' + B', A' + B' = A + B 

have been allowed to proceed is regarded by them as by no 

Chemical Ajfinitij. 185 

means the equilibrium of a system the parts of which are at 

So long as equal amounts of A' and B', and of A and B, 
are formed in unit time, so long is the equilibrium of the sys- 
tem maintained. 

Let it be supposed that the molecule A consist of the atoms 
(or molecules) a and 7, these atoms "will continually perform 
their proper vibrations within the molecule A. At certain 
positions of « and 7 we may suppose that the force acting 
between these two atoms is very small. Let another molecule 
B be composed of the atoms ^ and S, these atoms will also 
perform vibrations within B ; A and B will also each be pos- 
sessed of its own proper motion. If A and B approach each 
other at the moment when a and y and /3 and S are respec- 
tively at those positions at which the force between them is 
very small, then a chemical force may act between (3 and y 
and between a and S which shall result in the production of 
two new molecules A' and B'. The reverse action, resulting 
in the production of A and B, may be su]:)posed to take place 
in a manner similar to that whereby A' and B' have been 

A similar view may be taken of the formation of an additmi 
compound. The compound molecule ABC may be split up, 
under certain conditions, into A, B, and C, while by the simul- 
taneous recombination of the molecules A, B, and C new com- 
pound molecules of tlie form ABC may be produced. 

In order to determine the velocity of formation of the new 
substances in such cases as the preceding, let p and q repre- 
sent the number of the molecules of A and B in unit volume ; 
further, let a be the number of p molecules wliich are so con- 
ditioned that by coming into contact Avith the molecules B 
they suffer decomposition, and let h represent the number of q 
molecules which are similarly conditioned with regard to A . 
In unit A"olume there are therefore ap molecules of the sub- 
stance A, and hq molecules of the substance B, which bv their 
mutual meeting together are capable of being transformed into 
new substances. The frequency of the meeting of undecom- 
posed molecules will be represented by the product ap . bq, and 
the velocity of formation of the new substances by the equa- 

(f) . aphq^kpq, 
where k=^(f)ab. 

If it be required that three substances A, B, and C suffer 
mutual decomposition in order that a new compound be 
produced, and if the number of molecules of each in unit 
volume be JO, q, and ;• respectively, then, expressing the proper 

186 Mr. M. M. Pattison Muir on 

coefficient of the substances l)y a, h, and c, the expression for 
the velocity of formation of the new compound becomes 

cf) . aphqcr = kpqr, 

where k is again fak(Mi as representing tlie product of the co- 

The velocity of formation of an addition com})Ound consist- 
ing of a. molecules of A, /3 molecules of B, and y molecules of 
C, is expressed as follows : — 

^ . apap .... bqJiq .... crcr 

= kpYry, 

where k expresses tlie product of all the coefficients. 

The velocity-coefficient, as also the coefficients a, b, c, must 
be considered as dependent not only upon the nature of the 
substances in the system, but also upon the temperature ; the 
nature of this dependence can only be discovered by expe- 

If the velocity of formation of the new substances be thus 
found, it is only necessary to equalize the velocity of the two 
opposing reactions in order to arrive at the conditions of equi- 
librium of the system. 

The absolute velocity Avith which the chemical change pro- 
ceeds is evidently equal to the difference between the velocities 
of the two opposing reactions. 

It is evident that this development of the theory of mass- 
action supposes that the influence o^ secondary forces (p. 183) 
is overlooked. It is probable that the action of these forces 
may be disregarded when very dilute solutions of the reacting 
substances are employed. 

From their general treatment of the subject of chemical 
equilibrium, Guldberg and Waage have been led to regard 
those processes as complete in which chemical reactions si- 
multaneously proceed in two opposite directions. On the 
other hand, when but one of these opposing changes is accom- 
plished, they regard the process as incomplete. By withdraAval 
from the sphere of action of one or more of the products of the 
first part of the process, or by the occurrence of secondary 
reactions, or by the maintenance of the temperature within 
certain limits, or by the assumption, by the affinity-coefficient, 
of a value such that a condition of equilibrium is attained 
when extremely small quantities of the reacting bodies are 
present — by these circumstances the occurrence of the reverse 
action, and hence the completion of the chemical process, may 
be prevented. 

Chemical A^nity. 187 

The application of their general theory of mass-action is 
considered by Guldberw and AVaage ^^■ith reference to various 
classes of chemical systems. 

1. Systems consistiriff of four Soluble Substances. 

One pair of bodies A and B^ is decomposed into another 
pair Ai and B in accordance with the equation 
A + B, = Ai + B. 

If the amounts of the indiyidual substances (expressed for 
the sake of simplicity in equivalent units) which are present 
when equilibrium is established be represented bv p., />i, q, qi, 
and if V be the total volume of the solution, then the active 
masses are represented by 

£. £l £ and ^ 
y y ' y v' 

the velocity with which the formation of A and B proceeds 

and the velocity with which the formation of A^ and Bi |)ro- 
ceeds by 

Deducing the condition of equilibriumj and taking A- as 
= y , and ki= j^, then 

k^=kj-^ (1) 

If the original quantities of the four substances be P, Pi, 
Q, and Qi respectively, and if we suppose that equilibrium 
ensues when a quantity | of the substances A and B is de- 
composed, then 

/>=p-i. />i=Pi+r, 

V = Q + | and 7i = Q-|. 

Putting these values into equation (1) and taking 77 =«, we 


^_ 4P + Q0 + Pi + Q 
^ 2(/c-l) 

_ /r 4P + Qi) + Fi + Q V^ P iQ-z^Qi ... 

"^ V 1 2(«-i) J ^ K-l ' ' ' ^"^^ 


:\Ii-. .^r. M. ralli^uu Muir^// 

"vvlien K>i, ilio minus rsi^-n is eiiH)loyctlj and the i)Ositivc si^rn 

p r 

■vvlieu K<1. The value of ^ is jjositivc when k r> r.'- 

Q, Hi 

It' it be desired to study the influence of time upon the course 

of the reaction, it becomes necessary to introduce the absolute 

velocity. If .v be the amounts of A and Bi decomposed to Aj 

and B in time t, then the amounts decomposed in an infinitely 

short time cU is il.v, and the velocity is ---. 

By further developmentj and by integration, the following 
formula is found : — 


gnat.(^..^)=0^jf(«-l)(A-^)./, . (3) 

K — 1 

From this equation it would appear that .r attains the value 
f only after an infinite time ; but the function in equation (3) 
is of such a character that the difterence between .v and ^ be- 
comes so small after a comparatively short time, that it may 
be disregarded in an experiment. 

The first special cases considered by Guldberg and Waage 

as illustrative of the systems now under examination is that in 

which A= acetic acid, B = Avater, Ai= ether, Bi= alcohol. 

From the experiments of Berthelot and St. Giles it may be 

sho^\Ti that -7- = 4. 

^1 . . 
The values given in the following Table for ^ have been cal- 
culated by the aid of equation (2). The secondary reactions in 
this special case exert a considerable influence upon the primary 
chemical chanoe. 

Initial quantities of 

Quantity of acetic acid 

Acetic acid. 




Obserred. Calculated. 
?. 5. 








0005 0-667 
0-828 0-845 
0-902 0-930 
0-858 0-845 
0-521 0-492 
0-407 0-409 
0-116 0-131 
0-073 1 0-073 

CJiemic(d Ajfinitij. 


The authors also consider the special case in which A =: ferric 
chloride, Brrhj-drochloric acid, Ai = ferric oxide, and Bi = 
water; and also that in which A = nitric acid, B = sodium 
nitrate. A] = sulphuric acid, and Bi= sodium sulphate. The 
experimental data for the first case were accumulated by G. 
Wiedemann (Pogg. Ann. 1878), and those for the second case 
are taken from the researches of Thomsen. 

It is evident from equation (1) that the proportion ki : k is 
determined by experiment, but not the actual value of ^i and 
Ic. By carrying out analogous experiments with new systems 
A, B, A2, B2, (fcc, it is easy to determine the new proportion 
k^ &c. : k. If, now, k be taken as = 1, the relative values of 
ki, ^2, &c. are obtained in i-eference to the pair AB. A Table 
may be thus drawn up by the aid of which the conditions of 
equilibrium for those systems which any two pairs of bodies 
in the Table are capable of forming among themselves maybe 

Thus, if it be wished to calculate the conditions of equilibrium 
for the system Aj, Ag, B„ Bo, the equation is 


and the values of ky and A-j are found from the Table. 

The three folloAving Tables have been drawn up from data 
taken from Thomsen's researches. 

Hydrochloric acid. 
Nitric acid. 
Sulphuric acid. 
Oxalic acid. 
Phosphoric acid. 
Tartaric acid. 
Citric acid. 
Acetic acid. 
Boric acid. 

Table I. 
Relative values of k. 


KH2 SO4) 


C2 H4 02 


B. k. 

NaCl 1 

NaNOs 1 

i(Na2 SO4) 0-25 

f(Na, 0, O4) 0-0676 

Na H2 PO4 0-0625 

^{Q,R^^n,0,) 0-0025 

KCeH^NasO,) 0-0025 

Co H3 NaOs 0-0009 

NaBOa 0-0001 

Table II. 

Hydrochloric acid. 
Sulphuric acid. 


Metallic chloride. 
Metallic sulphate 

The metal may be potassium, sodium, or ammonium. 




190 Mr. i\I. 31. Pattison Muir on 

Table III. 

A. B. k. 

Hydrochloric acid. Metallic chloride. 1 

Sulphuric acid. Metallic sulphate. 0"5 

The metal may be magnesium, iron, manganese, nickel, 
cobalt, or copper. 

Table IV. 

A. B. k. 

■ R"C1. i(E2''S04). 1 

R'''C1. KtV"S04). 2 

H" = metal of Table II. U"' = metal of Table III. 

2. Si/stems consisting of tic o Insoluble and two Soluble 

In the case of insoluble compounds the active mass of the 
substance does not necessarily decrease in the same proj)ortion 
as the total mass of the substance present. Increase of the 
absolute amount of an insoluble substance does not increase the 
active mass of that substance to any sensible extent. Thus, 
1 orm. of an insoluble salt in lOO cub. centims. of liquid pro- 
duced the same effect as 2 grms. of the salt. 

Supposing, then, that the masses of the insoluble substances 
are constant during the experiments, these masses enter the 
equations as unknown constant quantities, the value of which 
mav be determined from the experimental data, either indepen- 
dentlv or along with other miknown constants. Under these 
conditions, the proportion between the amounts of the two so- 
luble substances is always the same when the system is in equi- 

The value of | is determined for the systems noAv under consi- 
deration by aid of the formula 

f=^^'. w 


(»i and (/i = masses of Aj and Bj, the soluble substances pre- 
sent). If the element of time be introduced, equation (4) 

Iognat.(ji;.)=^^\;,±-^'\/, ... (5) 
.r = amount of substance A^ transformed into Bj in time t. 

Chemical Affinitt/. 191 

3. Systems consisting of an indefinite Number of Soluble 

When several chemical reactions proceed simultaneously in 
the same solution, the velocity of each individual reaction is in- 
dependent of the other reaciions. 

The conditions of equilibrium for such a system are ex- 
pressed by the formula 

iP-J.Pl- J. P-2 _ 7, P« 

A/ — A 1 — A, 9 — • • • '^ n • 

? ?1 9-2 'In 

Putting ' =z, it may be shown that 

P + Q , Pi + Qi r 

q= y-p^, and q^= ^ &c 

The general equation is deduced 

^^' 1+^z 1+f 

The value of ;::can be found by aid of this equation, and from 
that the value of ^, QiyQn, ^nd finally the value of p, pi,...j->n. 

Several illustrations are given of the application of this for- 
mula ; but no experimental data have as yet been accumulated. 

As an example of the method of solving the problem j^re- 
sented by a system consisting of many soluble substances, the 
question is discussed : — How would one equivalent of soda 
divide itself between 1 equivalent of hydrochloric acid, 1 equi- 
valent of sulphuric acid, and 1 equivalent of oxalic acid ? 

Let the original system consist of 1 hydrochloric acid + 1 
sulphuric acid + 1 sodium sulphate; and let A = hydrochloric 
acid. A, = sulphuric acid, A2 = oxalic acid, B = sodium chloride, 
B-i = sodium sulphate, and 62 = sodium oxalate; then 

P=l, P, = l, P2 = 0, 

Q=0, Q, = o, q, = i. 

From Table I. (p. 189) the following values are found: — 

k = l, A', =0-25, A-2 = 0-0676. 
Equation (6) then gives 


+ ^—. — + . ..... =1. 

1+z 1+4.. z l + U-^.z 

By repeated trials of various values for Zy the approximate 
value of that proportion is found to be 0*62. Hence the 
following equivalent proportions are determined for the con- 

192 Mr. :\r. M. Pattisun ^Uuv on 

ditions of oquilibriuin ol' the .system : — 

Sodium chloride <j =0"()2 Hydrochloric acid /> =()*o8 
Sodium suljihate <ji =0"21> Sulphuric acid ... ;^i=i()-71 
Sodiuui oxalate q2 =0*10 Oxalicacid j>., = {)-[)0 

Of the remainin<T systems considered the more importjint 
are : — 

4. Sf/sU')ns consUtlng of gaseous suhstances arising from the 
dissociation of a solid ; and 5. Sgstems consisting entirely 
of gaseous substances. 

If a gas M be an addition compound of the form aA + /3B 
+ 7C, then, by dissociation, one molecule of this gas will be 
resolved into a molecules of A, /3 molecules of B, and 7 mole- 
cules of C. If, further, ]->, q, and r be the amounts of the 
different components in unit volume, and if the most general 
case be considered, in which, besides the amounts present of 
p, q, r (the dissociated constituents of M), an amount P of 
the oi'iginal compound is also present, then the equation of 
equilibrium is deduced, 

;AyV=c/,[P + F(0]. . •.-.•.• (7) 
This equation is also applicable to cases in which indifferent 
gases, other than A, B, or C are present. The equation is 
developed and applied by the authors especially to the results 
of experiments upon the dissociation of N2O4 into NO2 where 
the product of decomposition of the original compound is alone 
present, and to the dissociation of HI in presence of either of 
the products of decomposition (see Devilleand Troost, Compt. 
Rend. 1875, and A. Naumann, Berl. J3er. x. 2045 ; see also 
Lemoine, Ann. Chim. PJnjs. [5] xii. 145). 

In his earliest paper (Pogg. Ergzshd. viii.) Ostwald de- 
scribes the experimental method which he has adopted, viz. 
measurement of the change in specific volume of a liquid ; 
and shows that it is possible by this method to measure small 
amounts of chemical change occurring between those sub- 
stances solutions of which are mixed to form the li(juid in ques- 
tion. Thus, if the sj^ecific volumes of normal solutions of potas- 
sium sulphate and of nitric acid be determined, if these solu- 
tions he mixed, and if the specific volume of the mixed liquid 
be then determined, it is found that a certain amount of expan- 
sion has taken place, and that this expansion measures the 
amount of chemical action which has occurred*. Ostwald 

* K. Hofmann (Pogg. Ann. cxxxiii. 575, 1868) seems to have been the 
first who attempted to deduce measurements of chemical change from 
determinations of sp. vol. and of coefficients of refraction. His attempt, 
however, was not altogether successful. 

Chemical Apiu'dy. Ilt3 

shows that his method yields resuUs identical with those ob- 
tained by Thonisen by means of the thermochemical method. 

Ostwald has also determined the coefRcients of refraction of 
a series of normal solutions of acids and of bases, and the coeffi- 
cients of refraction of the liquids produced by mixing these ; 
and in this way he has arrived at results concerning the che- 
mical action between the acids and bases in question, which 
corroborate those obtained by the specific-volume method. 

When aqueous solutions of acids and bases are mixed in 
equivalent quantities, the volume of the product is different 
from that of the sum of the volumes of the constituents. This 
change of volume varies with the acid, the base, the tempera- 
ture, and the degree of concentration. The two latter con- 
ditions being kept constant, a value is obtained for each com- 
bination of acid and base. The normal temperature employed 
was 20° ; the normal concentration 1 equivalent (in grams) 
of the acid or base, in 1000 grams of the solution. 

In the general reaction A + B=A' + B', let A and A' be 
the acids, let B' be the neutral salt of the acid A, and B the 
neutral salt of the acid A' icith the same base ; then the coeffi- 
cient of affinity may be defined, for this reaction, as the pro- 
portion in which the base divides itself between the two acids 
when the three substances mutually react in equivalent quan- 
tities. The amount of base taken up by each acid is a measure 
of the affinity of the acid for the base; the coefficient of 
affinity expresses the relation between these affinities, or, in 
other words, the relative ajjinity of the acids for the base. 
The relative affinity of the acids is a function of their absolute 
affinity, and nmst be studied under those conditions which 
influence the latter. These conditions are nature of the base, 
temperature, and perhaps pressure. The latter was constant 
throughout the investigations to be described. 

Let the changes of volume occurring when the acids A and 
A' combine with the same base C be expressed bv v and v' . 
Let the acid A withdraw a portion x of the base, A' will with- 
draw l—.v. Then the resulting change of volume Vq will be 

fo=.a- + (l— .i-)i-', 

supposing, that is, that no change of volume is brought about 
by secondary reactions ; 

The greater the difference {v—v') between the changes of 
volume occurring in the neutralization of each of the acids 


Mr. M. M. rattisoii Mulr on 

separately, the more accurate will the determination of the di- 
vision of the same base between these acids become. 

In the reaction between the salt A'C and the acid A, whereby 
.r parts of A'C are decomposed with formation of ./• parts of 
AC, the changes of volume are v'x and i\c (the value of v'x is 
taken as negative because it represents a decomposition), and 
the observed volume-change in the liquid containing the react- 
ing bodies is ri = r.r — r'.r + f, where f expresses the sum of 
the secoiularv reactions. 

Similarly it is shown that the observed volume-change in the 
reverse action, viz. decomposition of ,r parts of AC by A', is 

v, = v'{l-,v)-v{l-.v) + ^. 

From these equations the value of .r is deduced, 

rj-iV <-i — «-2 

These equations are applied by Ostwald to the experimental 
results which he has obtained. . 

The relative affinities of sulphuric, hydrochloric, and nitric 
acids for the alkalies, magnesia, zinc oxide, and copper oxide 
are considered by Ostwald in his second paper. 

In the following tables v^ represents the volume-change 
accompanying the action of nitric or hydrochloric acid on the 
sulphates of the bases mentioned, r^ the volume-change ac- 
companving the action of sulphuric acid upon the nitrates or 
chlorides of the same bases, v — v' represents the calculated 
differences of the volume-changes caused by neutralization. 

Table I. 

Influence of Base. 

Nitric and Sulphuric Acids. 







+ 14-00 
+ 13-77 
+ 11-04 
+ 10-58 
+ 8-8G 
+ 7-85 


+ 10-38 
+ 10-.j() 


+ 1107 
1 +11-27 

+ l()-&4 
+ 16-50 
+ 14-49 
+ 13 35 
+ 12-54 
+ 10-G9 



Zinc oxide 

Copper oxide ... 

Chemical A^niti/. 


Table II. 

Influence of Base. 

IIi/drochlo7'ic and Siilj^hiiric Acids. 

1 Base. 





1 Potash 




. +13-08 
. +13-IK3 
. +11-45 
. +10-47 
+ 9-08 
. + 8-06 


+ 15-52 
+ 12-40 
+ 11-55 

+ 15-56 
+ 1.5-50 
+ 13-60 

Zinc oxide 

Copper oxide .. 

Table III. 

Yolume-clianges accompanying the action of Sulphuric Add 
upon Sulphates: RSO4 + /jH^ SO4. 

71 = 

i 1. 

2. , 4. 



+ 2-66 
+ 1-83 
+ 1-37 

+ 7-09 

+9 25 ! +9-80 

+ 9-06 
+ 7-93 
+ 6-77 
+ 501 
+ 3-26 



+ 8-98 



Zinc oxide 

Copper oxide.. 

Table IY. 

Volume-changes accompanying the action of Nitric Acid on 

Nitrates, and Hydrochloric Acid on Chlorides. 



Macruesia +0-07 


Zinc oxide +0-52 

Copper oxide +0-34 

In order to find from these data the value of .r in the equa- 

.(, , 

it is necessary to proceed by systematic trials, inasmuch as f 
is dependent upon .?-, hut the form of this dependence is un- 

* ^ is composed of the volume-changes accompariTing the reactions 
(1 -a;) RSO^+a-H.SO,, and xRNA+(i-a:)H,N,06'(or a^EOL+Cl-a?] 
HoClo) , in the case of the alkalies the last member of this gi-oup of 
chang-es =0. 


Mr. M. M. ratti.son Muir on 

By proceed in<r thus the following Table is prepared, hi 

this table colunm I. expresses the relative affinity -,/ ^^^y-^; 

column II. the relative atiinity ^r Qr>~? ^^^^ column 111. the 

relative affinity tt ir X -- 
^ H2N2OG 

The relative affinities of columns Land 11. are calculated i'roni 

the equation ^ = 7 — > mid tlioso of column 111. by dividing 
II. into L ^-''■' 

(On account of the smallness of the difference t'l — ^2? ^^^ 
affinities of Column III. could not be directly determined by 
the volumetric method.) 

Table V. 
Influence of bases upon Relative Affinities. 


J H,N,0, jj H,C1, 

III H,C1, 


0:667_o.oo 1 0-fi59_i.94 l-9^_o-97 





0-638 1 ^,, 
0-617 i.pi 

0-591 _, 
0-409 ^ 

0-341 2-00 
0«57_i.9^ l^--0-96 
0-343 2(10 
0-(;44_i.3i ' l-81^o.y, 
0-356 1-88 
0-635_j.^^ l"-^=0-99 
0-365 1-76 



Copper oxide . . . 





From these results it ap})ears that the afiinity-proportion 
H2 SO4 : Ho N2 Oc and Ho SO, : Ho Clo is dependent upon the 
nature of the base, but that H3 Clo : H^ No 0^ is independent 
of the base. From considerations ren-arding the ^•olume- 
changes accompanying the action of sulphuric acid upon sul- 
phates, Ostwald shows that the whole mass of this acid is not 
to be regarded in determining the affinity of the acid towards 
bases, but only that part which is not converted into acid sul- 
phate. Hence he concludes that probably the true relative 
affinity of snlplun-ic acid, as that of nitric and hydrochloric 
acids, is indei)endeiit of the nature of the base neutralized. 

The iniluencc of temperature upon the relative aiiinities of 
the acids is set forth in the following Tables : — 

Chemical Affimty. 

Table YI. 
luflueuce of Temperature. 


Citric and Sulplniric Acu 









+ 11-49 -3-39 
+ 13-77 -2-73 
+ 15-95 -2-15 
+ 1816 -1-29 

+ 14-88 
+ 16-50 
+ 18-10 
+19 45 

Hydrochloric and Sulphuric 






+ 10-79 
+ 12-99 
+ 15-36 
+ 17-77 


+ 13-76 
+ 15-51 
+ 18-81 








+ 4-11 
+ 6-32 
+ 9-15 

+ 11-74 

+ 5-46 
+ 8-33 
+ 11-62 
+ 14-94 

Table YII. 
Influence of Temperature upon Relative Affinities. 








=2 37 


HX'l , 


H.,C1 , 


= 1-93 

= 1-92 

= 1-99 










= 102 



= 100 

It is evident from these Tables that the relative affinities of 
hydrochloric and nitric acids are independent of the tempera- 
' Fhil. Mag. S. 5. Vol. 8. Xo. 48. Sept. 1879. P 


^Ir. M. M. Pattison Muir on 

turo, wliilo that of sulpliuric acid varlos with the temperature, 
hilt in a manner inversely as the bindin*^ of that acid by neu- 
tral sulphate (see Table VI.). 

From tliese results Ostwald concludes that most probably 
the relative o^mty of the acids is a constant numher indejiendent 
of hai<e, and independent of temperatnre ; he believes that this 
generalization holds good for all the acids. 

If the absolute affinity of an acid A for a base C be repre- 
sented as a function of both, the above generalization may be 
expressed in the form 

and from this it follows that 

/(AiC) _/(A/C). 

/(A,co /(A/cy 

i. e. the relative affinities of the bases are independent of the par- 
ticnlar acid used for neutralization. 

From these relations Ostwald deduces the result that the 
function /(AjC) is a product of two factors, one containing 
only Ai and one only C : 

/(A,C) = <^(A).,/r(C); 

or, tlie affinity hetiveen an acid and a base is a product of the spe- 
cijic afjinitij-constants of the acid and base. 

If the regularities observed for the special cases now de- 
scribed be regarded as expressing a true generalization, the 
affinities which come into play in the formation of salts may 
be simply expressed in a Tal)le such as that given below. 

The relative affinities of all bases being determined in refe- 
rence to one acid, and those of all acids in reference to one 
base, and the affinity of this acid to this base being taken as 
unit, the values so obtained may be arranged as follows : — 


<P (A'). 











^(C") ... 



^iC'") ... 





The product of the expression at the head of one of the 
horizontal columns, yjr (C), with that at the head of one of the 
vertical column, cf> (A), gives the magnitude of the affinity 

Chemical A^nity. 


exerted between the corresponding base and acid. By deve- 
loping the Table in a third direction in space, expression might 
be given to the influence of temperature upon the absolute 
aflfinity (-which influence is yet to be determined). The fact 
that temperature is without influence upon the relative affinity 
means only that the influence of temperature upon the abso- 
lute afiinity is the same for all compounds of acid and base. 

In his third paper Ostwald extends his researches upon the 
neutralization of acids by bases. The following Tables con- 
tain the principal results. 

The + sign denotes expansion of volume, the — sign con- 
traction ; the numbers in brackets [ ] express the differences 
between the sums of the coefficients of refraction of the acids 
and bases, determined separately, and the coefficient of re- 
fraction of the solutions formed on mixing these. The + sign 
indicates an increase, the — sign a decrease in the coefficient 
of refraction. The determinations of refraction-coefficients 
were made at 20°, the sodium light being employed. 

Table YIII. 
Neutralization of Monobasic Acids, 


Soda. 1 Ammonia. 

X^itric acid 

+20-046 [-897] +19-770[-886] - 6-441 [+139] 
+19-.521 [-882] 1 +19-238 [-879] - 6-572 [+148] 
+19-626 [-916] \ +19-.3.36 [-907] - 6-567 [+117] 
+19-799 [-938] ' +19335 [-923] - 6-442 [+100] 
+12 361 [-484] 1 +12-153 [-478] -13-593 [+.536] 
+ 9.522 [-363] • A- 9287 [-.3.541 -KVTil r + 6461 

Hydrochloi'ic acid ... 
Hydrobromic acid ... 

Formic acid 

Acetic acid 

Monochloracetic acid.. 
Dichloracetic acid . . . 
Trichloracetic acid . . . 

Propionic acid 

Butvrie acid 

+ 10-855 [-425 
+12-946 [-552] 
+17-357 [-774] 
+ 7-8.30 [-318] 
+ 6-984 [-279] 
+ 6-301 [-254] 
+ 9-616 [ - ] 
+ 8-267 [-353] 

+ 10 628 [-412] 
+ 12-702 [-544] 
+ 17-067 [-774] 
+ 7-679 [-306] 
+ 6-844 [-269] 

-15-087 [+603] 
-12-975 [+473] 
- 8-665 [+2t>4] 
-17-822 [+699] 
— 18-6:1^ r 4- T."^ 11 

Isobutrric acid 

+ 6-174 [-248] -19-270 [+758] 
+ 9-517 [ - ] - 16-496 [ -] 
+ 8-133 [-344] -17-7,39 +6611 

Glycollic acid 

Lactic acid 

^ ' 1 

If the values which the same acids give with difierent bases 
be considered, it is found that they are always positive [nega- 
tive] for potash and soda, and always negative [positive] for 
ammonia. The two following Tables contain the differences 
between the numbers obtained by neutralizing the same acid 
■nith two different bases, and the differences between the 
numbers obtained by neutralizing different acids with the same 

From these results it is seen that, the differences betiveeti 
the numhers found for any tico bases are nearly constant through- 



Mv. M. M. Pattison Muir on 

out the series of acids. Further, the dijferences hetween the 
numbers found for an^two acids are nearh/ constant for the three 

In Table X. the differences are those between the number 
found for isobutyric acid (which had the smallest observed 
value) and that for each of the other acids. 

In Table IX. the vertical columns represent the constant 
differences, in Table X. the horizontal lines. 

Table IX. 
Differences referred to Acids. 

Potash- Aramonia. 

Soda- Aramonia. 


Nitric acid 

26-487 [10.36 
26-093 [1030 
26-191 [103:3 
26-241 [1038 
25-954 [102<;» 
25-783 [1009 
25-942 [1028 
2.5-921 [102.5 
26 022 [103S 
25-652 [1017 
25-617 [1009' 

25 .572 [1012' 
26-112 [ — ' 

26 00(][1014' 


26-211 [1027] 
25-810 1027] 
25-901 [1024] 
2.5-977] 1023] 
25 746 [1014] 
25-.548 [10001 
25 715 [1015] 
25 677 [1017] 
26-732 [10;38] 
25-501 [10O5] 
25-477 [ 999] 
25-444 [1006] 
26-013 [ — ] 
25-872 [11X15] 

0-276 [ 9] 
0-28.3 [ 3] 
0-2i»0[ 9] 
0-2(>l [15] 
0-202 [ 7] 
0-235 [ 8] 
0-227 [13] 
0-244 [ 8] 
0-29(J[ 0] 
0-151 1 12] 
0-140 [10] 
0-137 [ 6] 
0099 [—] 
0134 [ 9] 

Ilyclroehloric acid ... 
Hydrobromic acid 
Hvdriodic acid 

Acetic acid 

Jloiiocliloracetic acid.. 

Dichloracetic acid 

Trichloracetic acid ... 
PfDijiouic acid 

Lactic acid 

Table X. 
Differences referred to Bases. 




13735 [<U3T 

13-696 [640] 

13064 [631 

13162 [6.59 

13-361 [67.5] 

6-019 [230] 

3-613 [106] 

4-454 [164] 

6-528 [196] 

12-893 [.526] 

1.505 [ .58] 

0-670 [ 21] 

0-000 [ 00] 

3.343 [ — ] 

1-959 [ 96] 

12-829 [619 

12 769 [610 

12-705 [641 

12-828 [(>58 

5 -(177 [222 

5-009 [112 

4-183 [155' 

6-295 [185 

10-605 [494' 

1-448 [ 59 

637 [ 25 

0-OCX»[ 00' 

2-774 [ — ■ 

1531[ 81] 

Hydrocldoric acid . . . 
Hydrobroraic acid ... 
Hydriodic acid 

13-220 [)>28 

13-325 [()62 

13-498 [684 

6-t)60 [230 

3-221 [109 

4-554 [171 

6-645 [198 

13-056 [520^ 

l-520[ 64 

0-683 [ 25' 

0-000 [ 00' 

3-315 [ — 

1-966 [ 99' 

Monochloracetic acid.. 
Dichloracetic acid ... 
Trichloracetic acid ... 
Propionic acid 

Butyric acid 

Isobutvric acid 

GlycoUic acid 

Lactic acid 

The constancy in the differences of the numbers found for 

Chemical AJfinity. 


acids and for bases is accounted for by Ostwald by tlic hypo- 
tbesis that the change of 2'>hyncal properties brought about by 
each substance entering into chemical combination is of constant 
value, and is independent of any alteration caused by the entrance 
into the coinpound of other substances. 

The volume-changes which accompany the action of mono- 
basic acids upon the normal salts of the same acids are shown 
to be very small. The volume-changes accompanying the 
action of one monobasic acid upon the normal salt of another 
acid are determined by Ostwald ; and by dividing the number 
so obtained by the ditference between the volume-changes 
noticed on neutralizing the base by each acid separately (a 
small correction being made for the action of the acid set free 
in the reaction upon its own normal salt), numbers are ob- 
tained representing the percentage amount of base taken up 
by the added acid. These numbers are contained in the fol- 
lowing Table, in which the first column contains the name of 
the normal salt, and the second that of the free acid added. 
One equivalent of free acid is always added to one equivalent 
of normal salt. 

Table XL 
Division of Base between two Monobasic Acids. 

Dichluracetate. Nitric acid 

Do. Hydrochloric acid . . . 

Do. Trichloracetic acid ... 

Do. Lactic acid 

Monochloracetate. TrichloraL-etic acid 

Formate. Trichloracetic acid... 

Do. Lactic acid 

Do. Acetic acid 

Do. Butyric acid 

Do. Isobutyric acid 

Butyrate. Acetic acid 

Isobutyrate. Acetic acid 

Propionate. Formic acid 

GljxoUate. Formic acid 






























































A similar table is given by Ostwald containing his results 
obtained by the chemico-optical method ; the general results 
agree very well with those of Table XI. 

Taking the affinity of nitric acid as 100, and that of hydro- 

202 On Chemical Afjinitij. 

chloric acid as D8*, the affinity of dicbloracetic acid is 

24 . . 26 

^P X 100 = 32, or, starting from hydrochloric acid, ^. x 98 = 3-4. 

In this manner the following Table is framed : — 

Table XII. 
Relative Affinities. 

Nitric acid 100 Fonnic acid 39 

Hydrochloric acid 98 Lactic acid '6'A 

Tridiloracetic acid 80 Acetic acid r23 

Dicbloracetic acid 33 Propionic acid 104 

Monochloracetic acid ... 7"0 Butyric acid 098 

Glycollic acid 50 Lsobutyric acid 092 

The order of the acids as arranged in this Table is regarded 
by Ostwald as correct ; but he believes that further researches 
will necessitate considerable changes in the numbers for the 
individual acids. 

The entrance of chlorine largely increases the affinity of tlie 
acid : this is shown by the numbers 1-23, 7*0, 33, and 80 for 
acetic, monochloracetic, dicbloracetic, and trichloracetic acids 
respectively. Similarly the entrance of oxygen into the mo- 
lecule of the acid increases the affinity f; while the addition of 
CHj decreases the affinity, as shown in the series of acids from 
formic to butyric, and also in glycollic and lactic acids. 

The importance of the results obtained by Guldberg and 
Waage, and by Ostwald, must be apparent to every chemist. 

In both series of researches we are taught of a coefficient of 
affinity which is a fixed quantity for each chemical molecule ; 
but at the same time we are led to recognize the paramount 
importance of the physical conditions under which this affinity 
is exercised. 

We are further presented with a tolerably satisfactory expla- 
nation of the leading facts of chemical action, without the 
necessity of appealing to any special and mystical " force of 
attraction " to account for these facts. 

The modern advances in the theory of chemical action lead 
us back more to the writings of Berthollet than to those of 
Bergmann. Bergmann's idea that the affinity of different 
substances may be represented by the amounts of each which 
combine together, was evidently untenable in the fuller light 

* This result is arrived at by Ostwald's own researches and by those 
of Thomsen, Pogg. Ann. cxxxviii. 05. 

t This is further shown by the numbers obtained for the relative affi- 
nities of succinic, malic, and tartaric acids, which are l-iS, 2'82, and 5*2 

On the Distribution of Heat in the Visible Spectrum. 203 

of the atomic theory. A modified form of Berthollet's asser- 
tion that the affinity of an acid is greatest for that base with 
M'hich it combines in smallest quantitj^, seems to be suggested 
by Thomson's results (confirmed by Ostwald's yolumetric 
method) that large affinity-yalue is accompanied by low heat 
of neutralization. 

Ostwald furnishes chemistry with a new method for solying 
some of her most difficult problems ; and Guldberg and Waage 
lead the way in the application of mathematical reasoning to 
the facts of chemical science. 

XXIII. The Distribution of Heat in the Visible Spectrum. 
By Sir John Conroy, Bart., M.A.* 

IN a paper " On the Distribution of Heat in the Spectrum/' 
originally published in the Philosophical Magazine for 
August 1872, and since reprinted in a volume of ' Scientific 
Memoirs/ Dr. J. W. Draper states the theoretical reasons for 
supposing that all the rays in the spectrum haye the same heat- 
ing efli'ect, in the following words : — " A given series of waves 
of ]'ed light impinging upon an extinguishing surface will pro- 
duce a definite amount of heat ; and a similar series of violet 
waves should produce the same amount; for though an undu- 
lation of the latter may have only half the length of one of the 
former, and therefore only half its vis viva, yet in consequence 
of the equal velocity of waves of every colour, the impacts or 
impulses of the violet series will be twice as frequent as those 
of the red. The same principle applies to any intermediate 
colour ; and hence it follows that every colour ought to have 
the same heating effect." 

Dr. Draper gives an account of some experiments he has 
made on the distribution of heat in the visible spectrum of 
sunlight. He finds that if the visible spectrum between A 
and Ho be divided into two equal portions, and all the light of 
wave-lengths between 7604 and 5768 be collected together, 
and also all that of wave-lengths between 5768 and 3933, the 
heat-intensity of these two series of undulations as determined 
by the thermopile are equal. 

The distribution of heat in the spectrum of sunlight had 
been previously experimentally investigated by Sir W. Her- 
schel (Phil. Trans. 1800, p. 255), J. Miiller (Pogg. Ann. cv. 

* Communicated by the Physical Society, having been read at the 
Meeting- held on June 28. 

204 Sir Jolm Conroy on the Distribution 

p. 337), Franz (Pog^. Ann. cxv. p. 2G0), Knoblauch (Pogg. 
Ann. cxx. p. 177, and cxxxvi. p. 6G), Fizeau and Fouciiult 
{Comjyti's Iiendus,xw. p. 447, and reprinted in the Anna les cle 
Chiniie, 5tli series, xv. p. 3(53), Desains ( Comptes liendus, Ixvii. 
p. -2117, and Ixx. p. 985), Laniansky (Pogg. Ann. cxlvi. p. 200). 
•Similar measurements were made with the limelight by Des- 
ains {loc. cit.) and Lamansky {loc. cif), and ot" the electric 
light by Professor Tyndall (Phil. Trans. 1«(>(J, p. 1). They 
all found but slight indications of heat in the violet and blue 
regions of the spectrum, the amount increasing in the green, 
yellow, and red, and attaining a maximum at a point beyond 
the end of the visible spectrum. 

The experiments were all made by placing a thermometer 
(one of the ordinary construction being used by Sir W. Her- 
schel and MM. Fizeau and Foucault, and a thermopile and 
galvanometer by the other observers) in various parts of the 
dispersion-spectrum formed by prisms of either glass, rock-salt, 
or sylvine. As Dr. Draper points out in the paper already 
referred to, this method appears to be an essentially defective 
one, as, owing to the unecpial dispersion by the prism of rays 
of ditferent refrangibility, a greater number of undulations of 
different wave-lengths must have been incident upon the sur- 
face of the thermometer when it was [)laced in the red and yel- 
low portions of the spectrum than when placed in the green, 
blue, or violet portions ; and the amount of heat indicated 
by the instrument being in proj)ortion to the amount of radiant 
energy incident upon its surface, the unequal dispersion of the 
prism would be sufficient to account for some difference in 
the heating effects produced by different portions of the spec- 

A graphical method appearing to afford the readiest means 
of determining the proljable effect produced by the unequal 
dispersion of the prism, a tracing was made, on paper divided 
into squares of ^,7 inch, of the curve representing the intensity 
of the heat in different portions of the visible spectrum, as deter- 
mined by MM. Fizeau and Foucault {Ann. de CJiini. 5 ser. xv. 
p. 377) — the position of the fixed lines in the spectrum, as 
given by them, being marked on one edge of the paper, which 
was taken as the .«• axis, and a scale of wave-lengths in ''tenth- 
metres " laid down at riy-lit antrles to this, and the curve for 
the dispersion of the prism constructed in the ordinaiy manner. 
At nineteen equidistant points in the spectrum the ordinates 
of the disjiersion-curve were measured in wave-lengths ; the 
difference between any two of them gave, approximately, the 
dispersion of the prism for that portion of the spectrum. A 

of Heat in the Visible Spectrum. 205 

difference of wave-length of 100 was taken as the unit, and 
the difference between the vakies of the ordinates divided by 
100 considered as a measure of the dispersion. The ordinates 

of the heat-curve of MM. Fizeau and Foucault at eighteen 
points in the spectrum, midway between those at which the 
ordinates of the dispersion-curv'e had been taken, were mea- 
sured in tenths of an inch, these numbers divided by those 
representing the dispersive power of the prism, and the quo- 
tients taken as gi%'ing the true relative intensity of the heat at 
the diftei-ent points of the spectrum. 


Sir John Conroy on the Distribution 

Ordinates of 


Ordinates of 


the dieper- 

divided by 100 

the heat-curve 








4-7— B. 




40— C. 








5-5— D. 








4-3— E. 



























2-2— G. 





















The Table shows that the numbers thus obtained for the 
intensity of the heat in ditterent ])ortions of the spet'truni lie 
close together ibr the region between B and F, the maximum 
being near D, and that from F to H the intensity diminishes. 

It would further appear that the curve for the distribution of 
heat of MM. Fizeau and Foucault is in reality a dispersion- 
curve, drawn to some scale of wave-lengths, for the particular 
prism used by them; and the diagram shows how very similar 
the curves for the intensity of the heat, and for the dispersion 
of the prism are to one another. 

The heat-curve reaches the x axis at a short distance on the 
more refrangible side of H2, the wave-length of that line being 
3932. The axis was taken as 3900 on the scale of wave-lengths 
to which the curve is drawn, and therefore the ordinate of 
the curve at B, measured in tenths of an inch, as proportional 
to the difference between this number and the wave-length of 
B, and the height of the ordinates at the other lines calculated 
on this assumption. 










... 2-10 

.. 1-87 

... 1-34 

,.. -95 

.. -88 

.. -63 

• 9-? 




Mean difference ... +'04 


of Heat in the Vuible Spectrum. 207 

Considering the nature of the data, and especially the small 
scale of MM. Fizeau and Foucault's diagram (the portion re- 
presenting the visible spectrum being only about 4 inches 
long), the measured and calculated numbers agree fairly well 

The same process was applied to the curves given by La- 
manskv (Fogg. Ann. cxlvi. p. 200) for the distribution of heat 
in the solar spectrum, with flint-glass and rock-salt prisms. 


s prism. 



Ordinates of the 

Ordinates of the 






8-4 ^• 


. CvO-I^ 




. 6;0 



11-8 ^ 



• '-9 F 
. 9-2""^ 



20-9 , 



. 8-2 

• ''•3 t;^ 

. 7-1 ^ 







. 5-8 



14-7 T. 



. 5-0 
. 4-4 p 



— It 










7-1 n 

Assuming the curves to be the dispersion-curves for the 
prisms, the ordinates were measured and calculated as in the 
former case. 



Flint-glass prism. 
Measured. Calculated. 





Rock-salt prism. 
Measured. Calculated. 






In none of the other measurements that have been made of 
the heat-spectra, as far as I am aware, are the positions of the 
solar hnes stated ; and therefore part of the data for eliminating 
the action of the unequal dispersion of the prisms is wantino-. 

An attempt was made to deal v/ith Knoblauch's measure- 

208 On the Distribution of Heat in the Vinible Spectrum. 

inents of the solar spectrum, and with Tyndall's of that of the 
electric light, by the same method. 

In both cases the experiments were made with rock-salt 
prisms ; and these were assumed to have the same disi)ersivo 
power as the one used by Lamansky, and the curve ])lotted 
accordingly. Two sets of measurements are given by Knob- 
lauch ; and the mean of these was taken for the following cal- 





Ordinates of 

Ordinates of 








lG-1 .. 

... 2-3 

28-3 ... 

... 3-0 

12-0 .. 

... 3-6— D. 

21-0 ... 

... 3-0 

8-7 .. 

... 3-9 

15-7 ... 

... 4-7— D. 

7-5 .. 

;:; 4-6-^- 

12-0 ... 

... 5-4 

7-0 .. 

8-2 ... 

... 5-7 p 

6-8 .. 

... 4-8 

0-5 ... 

6-6 .. 
(5-3 .. 

... 4-7 p 

5-0 ... 
3-5 ... 

... 3-5 
... 2-5_p 
... I'i 

6-0 .. 

.... 4-0 

2-0 ... 

5-7 .. 

.... 4-0 

1-5 .. 

... M 

•9 .. 

... -G 

The nature of the available data is such that the only defi- 
nite conclusions which it is possible to draw from these calcu- 
lations are, that the distribution of heat in the normal spectrum 
differs greatly from that in the dispersion-spectrum, and that 
in the dispersion-spectrum the great calorific intensity of the 
red rays, and therefore in all probability of the invisible rays 
beyond them, is due to the action of the prism in concentra- 
ting these rays upon the face of the thermopile. The intensit}'- 
of the heat in the different portions of the normal spectrum, 
except in the case of Lamansky's measurements with the flint- 
glass prism, apparently varies but little through a considerable 
space; and this affords some support to Dr. Draper's hypo- 
thesis, that every colour ought to have the same heating 

After I had finished these calculations, I found that G. 
Lundquist had investigated (Pogg. Ann. civ. p. 14G), from 
Lamansky's measurements, the distribution of heat in the 
normal spectrum, and had shown that it differed greatly from 
the distribution in the dispersion-spectrum — the maximum 
intensity in the case of the flint-glass prism being near D, and 
in the rock-salt prism near E. He also found from Tyndall's 

0)1 Structures in an Earthquake Country. 209 

measurements of the heat of the electric-light spectrum, that 
in the normal spectrum the maximum was near A. 

Lundquist arrived at these results by a mathematical pro- 
cess, based on the same general principles as the graphical 
one I have employed. 

XXIV. On Structures in an Earthquake Country. By John 
Pekby and W. E. Ayrton, Professors in the Imperial Col- 
lege of Engineering J Japan*. 

IN a country like Japan, where several sharp earthquakes 
occur yearly, where there are between three and four 
hundred destructive earthquakes on record, and where over a 
hundred thousand people are said to have been killed in one 
almost continued earthquake lasting for a month, and which 
occurred so recently as 1855, the question of the stability of 
structure is all-important. 

When working at our paper " On a neglected Principle that 
may be employed in Earthquake Measurements,''^ read before 
the Asiatic Society of Japan on the 23rd of May, 1877, and 
which appeared in the Number of the Philosophical Magazine 
for July 1879, we were led to consider how the effect produced 
by an earthquake on a structure is influenced by the time of 
vibration of the structure. 

It follows from that principle that if a number of quickly 
vibrating bodies form part of the same structure, they all 
vibrate in much the same way; that is, the periods of their 
swings are all approximately equal to one another and equal 
to the periods of ihe earthquake ; and although they differ in 
the amount of their motions, these amounts and their differ- 
ences are all exceedingly small ; whereas if one or more of the 
parts of the sti'ucture are only capable of vibrating slowly, the 
periods of vibration of the different, parts vary very much, the 
amounts of the motions are all comparatively great, and their dif- 
ferences are all relatively considerable. If, however, there is a 
sufficiently great viscous resistance to motion of such slowly vi- 
brating parts, these parts will be found during an earthquake to 
behave much as if their natural periods of vibration were quick. 
Supposing the foundation of a structure to vibrate with the 
earth which encloses it, we see that a slowly vibrating struc- 
ture which is fastened to these foundations is during an earth- 
quake subjected to stresses which may be excessively great 
and of a very complicated kind, whereas a quickly vibrating 
structure is subjected to stresses which may be said to be de- 

* Communicated by the Authors. 

210 Professors Perry and Ayrton on Structures 

terminate, and wliieh are coniparatlvi'ly small. It is not hero 
necessary to considei" whetlicr, as all the motions of a quickly 
vibrating body must be small, such a structure will be more 
comfortable to live in, because it is doubtful whether the an- 
noyance produced by rapidity of shock would not more than 
counterbalance the annoyance of great but smooth motions. 
It is only safety we are here considering ; and in this respect 
there can be no doubt of the superiority of rigid structures, 
or of structures having a sufKciently great viscous resistance 
to motion. Some calculations which we have made of the 
times of vibration of ordinary structures, such as well-built 
houses of stone and brick, chimneys, lighthouses, &c., will be 
found at the end of this paper ; and from these we see that 
the periods are all much less than what we judge from our ex- 
perience is the ordinary period of vibration of earthquakes in 
Japan. Even two-storied houses built of wood, if framed in 
the best way, have quick times of vibration ; such structures 
are therefore, it seems to us, well capable of resisting the ordi- 
nary Japanese earthquake-shock. As, however, •vve have not 
yet experienced the effects of a destructive earthquake, and as 
we presume that one of the most important ways in which 
it may difler from ordinary earthquakes is in the suddenness 
of motion, or change of motion, it cannot be said that any or- 
dinary structure has a quicker period of vibration than a 
destructive earthquake ; consequently, if it be granted that 
stability depends on the structure having a quicker period of 
vibration than that of the earthquake, the stability of a 
building will be only relative. We can of course be sure that 
by making the walls of a building thicker and its height less, 
we add to its safety; but however tar we may go in this direc- 
tion, we cannot be certain but that after all the earthquake- 
period may be less than that of our building. 

We must therefore content ourselves with saying that a slowly 
vibrating structure will probably get broken in its connexions 
with the foundations if these be rigidlv fixed to the ground: 
consequently (and we here oppose the })ractice of many archi- 
tects and engineers) putting a heavy top to a lighthouse, the 
chimney of a factory, or other high building, must certainly 
tiike from its stability. 

And although we see from the calculations at the end of the 
paper to which we have referred, that the times of vibrations 
of ordinary brick and stone houses are very short, still, in view 
of the possible great suddenness of a destructive earthquake, we 
should advise that all buildings be kept as low and made as 
rigid as possible. 

The argument used by engineers to support the practice 

in an Eartliquahe Ctnintnj. 211 

above referred to, of placing a heavy top on a chimney, as- 
sumes that the shock is an impact, and consequently that a 
definite quantity of momentum is given to the structure ; but 
it must be quite evident that it is the relative velocity of the 
base of the structure with regard to the other parts which is 
the fixed quantity, and therefore that the moi'C massive the 
structui-e, the more momentum enters it through the base. 

There is no easy way of judging what are the forces which 
cause an ordinary Japanese house to return to the perpendi- 
cular position after it has received a push or blow ; and so we 
cannot calculate its natural time of vibration ; but it is well 
known that it vibrates very slowly, an ordinary Japanese two- 
storied house with the usual heavy roof taking perhaps four 
seconds to make a complete vibration. The restoring forces 
are due merely to stiffness of the joints, there being no 
rigid connexion with the ground, since the vertical posts of the 
house are all supported on detached stones, and there are also 
no diagonal stays in the building. Such a structure is there- 
fore capable of being displaced very far from its position of 
equilibrium without fracture occurring ; and as its time of vi- 
bration is very long, it has a very great amplitude of swing 
during most ordinary earthquakes. That this amplitude is not ' 
even greater is most probably due to the fact that there is a 
sort of v.'scous resistance to motion at all its joints. Such a 
viscous resistance must greatly diminish the motion, and will 
be especially useful in an earthquake consisting of regular vi- 
brations; but the most severe test of such a structure consists 
in an earthquake-shock which begins with a sharpe impulse, 
or Avhich has a very irregular motion. The slowly vibrating 
structure would register the shock in a longer period of time 
than that in which the blow was delivered ; but it would pro- 
bably have an exceeding great first s^nng from its position of 

We think that the important elements of safety in ordinary 
Japanese structures is this viscous resistance which they oppose 
to motion, and which is mainly due to the great multiplicity o 
joints (all of which are compelled to move) and to the absence o 
diagonal pieces ; for we deduced from the principle in our ori- 
ginal paper, that if the restoring forces are weak there ought 
to be a great viscous resistance tomotionif we wish the strains 
of the structure to be small. But it must be remembered that 
this safety is only gained by a veiy great expenditure of timber; 
so that, although such slowly vibrating structures as many of 
the temples in this country may be regarded as exceedingly 
safe during earthquakes, it must not be concluded that all 
heavily roofed houses are secure. 

212 Professors Perry and Ayrtoii on Structures 

The amount of momentum which has to be transmitted 
through the founthitions of a l)uilding to the superstructure 
depends on the nature of the earthquake (that is, its sudden- 
ness and the amount of earth-motion), as well as on the mass of 
the building, while the velocity of the foundations, if these are 
rigidly connected with the earth, is inde|)endent of the mass 
of the building — an important fact to which we have already 
drawn attention. The earthquake energy gets destroyed by 
the interior portions of the earth, as well as the mountains and 
buildings at its surface not having exceedingly small periodic 
times of vibration, in consequence of which interference takes 
place at every sm'face of contact of the ditferent portions. Of 
course, however, any one particular building will destroy only 
a very small portion of the whole energy of the earthquake- 
vibration; so that its mass cannot in any perceptible way affect 
the motions of its foundations. 

In the same way as we have shown that the more quickly 
a house is capable of vibrating the less is its motion rela- 
tive to the foundation, we might arrive at the result that 
the smaller the natural period of vibration of the several 
portions of a body subjected to shocks, the less internal fric- 
tion must there be ; and this conclusion is consistent with the 
•well-known fact that there is more internal friction in non- 
homogeneous bodies, or rather, we should say, in bodies which, 
being non-homogeneous, have some of their materials only 
capable of very slow natural vibrations compared with the 

We have no doubt that with any given material what- 
ever there is a best method of constructing buildings in an 
earthquake country. Thus, with small stones set in bad mor- 
tar, or in no mortar, as in the buildings destroyed by the Nea- 
politan earthquake of 1857, the momentum which must pass 
through any level joint depends (1) on the short time Kluring 
which the foundations are acquiring a great velocity r, (2) on 
the mass of the building M above the joint, and (o) on the 
natural time of vibration of the portion of the structure be- 
tween the given joint and the foundations. If this time of 
vibration is very short, then the momentum Mr must be trans- 
mitted by the joint in the short time t ; that is, the joint must 

transmit the great force -— ; whereas if the time of vibration 

of the building below the joint is considerable, the time of 
transmission of momentum is increased in a calculable way, 
say to the time iit, and hence the force transmitted by the 

joint becomes reduced to — • It is for this reason that, if we 

in an Karthqnake Coantri/. 213 

^vish to drive in a nail without hurting the head with the 
hammer, a block of wood is used as a cushion, the wood being 
of service because, having an ap})reciable time of vibration, it 
causes the duration of the impact to be lengthened, and so di- 
minishes the force acting at any moment. Similarly, the baro- 
meters in men-of-war are not now suspended direct to the 
ship's sides, but to the end of a flexible lath, in order to prevent 
the shock accompanying the firing of the guns breaking the 
barometer-tube. In the same way, the lower parts of a struc- 
ture having appreciable times of vibration cause the earth- 
quake-shock to be altered in character, to 1)6 lengthened in 
time, and therefore diminished in intensity before it reaches 
the upper parts. Hence it is obvious that if small stones or 
bricks set in bad common mortar are our building mate- 
rials, it would be better to choose for the site a quaking bog 
which was capable of supporting the weight of the building, 
rather than to build the house direct from a rocky foundation ; 
or if the ground is firm, there ought to be placed underneath 
the house a foundation of yielding timber ; or some other 
method should be sought for by means of M'hich the time of 
transmission of momentum throujj'h the joints may be in- 

Thus, there is a best time of vibration of the part of a struc- 
ture below a joint, which depends on the strength of the joint; 
and if the basement has a time of vibration different from this, 
then we should advise that the building be kept low. For ex- 
ample, it is desirable that houses with ordinary wall-thicknesses 
built of bricks set in common mortar should not be more than 
one or, at the ^'ery most, two stories high if there is a piled 
or concrete foundation ; but if good cement be employed in- 
stead of bad mortar in fastening the bricks together, then a 
height of two or three stories may be employed probably with 
comparative safety. 

Again, the horizontal vibration of the ground is given up 
to a stone or brick building mainly by shearing-stress com- 
municated from course to course, a kind of stress which mortar 
is very unsuitable to transmit. Hence a stone or brick build- 
ing subjected to horizontal shocks ought certainly to be built 
w'ith cement and not with ordinary mortar. In fact, in every 
part it ought to be capable of resisting pulling as well as 
crushing stresses. 

Every joint is a weak place ; and it is evident that if by in- 
creasing the size of the building we diminish the area of joints, 
we shall be increasing the stability. Xow in large masonry 
structures larger stones are, as a rule, employed, and the joints 
are made of less area. In this respect, then, mav we say that 
■ Pliil Mag. S. 5. Vol. 8. Xo. 48. Sept. 1870. ' Q 

21 t rrolossors Pcny cnul Ayrloii o>i Slrnctincfi 

largo mnsoni'v structures l)uilt with coiiiiiion mortar arc usually 
more stal)lo than smaller ones. 

It is quite evident that as a concrete can be ohtained which 
will resist as great a tensile stress as ordinary brick itself, we 
shall derive great benefit from making all horizontal sections, 
of a structure which is composed of bricks set in good cement, 
as great as possible; that is, we shall find that the most suit- 
able structure, if of brick or stone, for an eartlujuako country 
must be comj)osed of large stones set in good cement with 
walls as thick as ])ossible near the base, the thickness of wall 
at every place being roughly proportional to the mass of the 
building above that place. 

As, however, the resistance to tension of timber is very 
much superior to that of cement or bricks, and as the mass of 
a timber l)uilding is small, a timber building with sufficiently 
strong joints must be very much superior to any structure of 
brick or masonry. And for the same reason a building of 
wrought iron might be made stronger still, and one of steel 
strongest of all. 

Ordinary timber houses ought not to be too rigidly fastened 
to the earth : if the joints of the structure are made, however, 
very strong, and especially if wrought iron is used as well as 
w^ood, and if there is diagonal bracing, then the connexions with 
the ground may be made more rigid. The stiffness of structures 
varies so much that we cannot give more definite rules than 
those contained in this short article ; but it is obvious that our 
principle of relative vibrations may be easily applied to find 
the best arrangement in a structure for any given material and 
with any given foundation. 

Calculations of Tunes of Vibration of (liferent Buildings. 

Since a square or circular building has usually the same 
period of vibration in all directions perpendicular to its height, 
it is not necessary to specify in which direction it is vibrating. 
Let us consider a prismatic structure of height h well built 
into the ground and of uniform horizontal section A. Let K 
be the radius of iivration of the section about an axis through 
the centre of the building ; then, taking into account bending 
and shearing stresses, a horizontal force P applied at the centre 
of gravity of the prism produces a deflection of the centre of 
gravity equal to 

P A^ P j^ 
EAK2'24"^ a'2N' 

where E is the modulus of elasticity of the material, and N the 
modulus of rigiditv, which latter is about one third of the former 

in an Earthquake Country. 215 

for building material. Consequently the deflection of the centre 
of gravity is equal to 


so that if, for simplicity, we suppose the prism to vibrate as if 
its mass were gathered at its centre of gravity, if T is the period 
of a complete natural vibration, and if w is the weight of the 
material per unit volume, 


PA f _A^ 31 


T=2W .;e\24K^ + 2/ 

For a solid rectangular structure with a square horizontal 
section of breadth b, 

^ "12' 


T=27r-i/^|i; + H 
V (7E \ 26- ^ 2 / 

For a hollow square section, the sides of the outer and inner 
square being respectively a and c, 

T7-2^__ a c 


2 1 2 

a + c 

Now for brick 

ic = ll2 1bs. '] 

and ^ about; 

E = 144,000,000 lbs. per square foot J 

.-. T=0-001534Aa /H-^ +3^ 
V 2\«- + c'-^ /* 


21() On Stt'iictnvP!^ in an KartJupiake Conntri/. 

S'jiiare house tcith no roof. 
Let //=30 foot, a = 30 feet, c = 2G feet; then 

T = 0-001534//4 /V ^<^^Q +3') 

V 2Vi)00 + 676 / 

= 0'06120 second aLont. 

This result may be taken as ajiproxiniately correct even for 
rooted bouses, because in a small house the roof gives stiffness 
as woll as adding inertia. 

When the hei<iht of the buildinfi is not more than twice or 
three times the outside horizontal dimensions, the shearing 
strains are important, and must be included in the calculations, 
as we have done. But when the height becomes eight or more 
times the horizontal dimensions, as in the case of a chimney, 
then Ave may neglect shear stress and consider bending only. 

Tall Cliimney. 
Let A = loO feet, a =10 feet, and o = 4 feet — that is, let us 
consider a thick square chimney; then 

T=0-001534 + 150y/l^?2gr^, 

= 2*301 seconds, about. 
If the chimney has the same internal dimensions, but if the 
brickwork is thinner than we have taken it, then a is less and 
T becomes still greater. Even, therefore, without the heavy 
top that some engineers have recommended to be added, this 
structure vibrates too slowly to be sufficiently safe in a country 
visited by frequent earthquakes, like Japan ; and Ave think it 
quite likely that the first really severe shock which maybe expe- 
rienced by the various chimneys recently erected in this country 
will destro}- them. It may here be noticed that even in 
England it is not thought to be saf<> to connect a tall factory- 
chimney with the main walls of a building ; so that, remem- 
bering the verv great difference in the time of vibration of the 
chimney and the walls, such a connexion nmst be regarded as 
exceedingly unsafe in Japan. 

Let us consider a conical mountain, then it is clear that in 
its vibrations shearing-stresses need alone be considered. A 
liorizontal force P acting at the centre of gravity produces the 

rh ^ chv 

On the Passage of the Galvanic Current through Iron. 217 

where r is the radius of the mountain at any distance x from 
the vertex, and N the modulus of rioidity. 

Now if a is the radius of the base, then at any distance x from 
the vertex the radius is 



Assuming, as before, that N is equal to one third of E, we have 
for the deflection produced by the horizontal force acting at the 
centre of gravity of the mountain 
r^ 'dYdx 

1' ' 





V 2aE 

= 0'00107 X h approximately. 

Hence a cone in which the diameter of the base is not much 
less than its height makes a complete vibration in one second 
if its height is 1000 feet; and the times of vibrations of such 
coues and pyramids are proportional to their heights. 

A large cone, however, would not receive the earthquake- 
shock as a house does, because the house receives the vibra- 
tion at every portion of its base almost simultaneously; so 
that it is difficult from the equation concerning the vibrations 
of buildings to predicate the production of cracks at the base 
of mountains. In fact, the question must Ije treated in a dif- 
ferent way, the propagation of vertical and horizontal strains 
being considered. It is evident, however, that unless the 
earthquake is of a suddenness such as we cannot comprehend, 
no fracture will be produced at the base of a hill or pyramid 
of, say, 100 feet in height. 

XXV. On the Passage of the Galvanic Current through Iron. 
Bij Felix Auekbach, Ph.D., of Breslau. 

[Coutinued from p. 152.] 

§ 8. AirE have yet to reply to the question whether the theory 
* T above sketched conditions an injiuence upon the fun- 
damental laws of galvanism, as well as npon the gnlvanic C07istants 
of iron, and, in the case of an affirmatives answer, how this 
influence asserts itself. 

218 Dr. F. Auerbach on the Passage of 

TLat such an influence nnist be present tlie following con- 
sideration shows. In the fundamental laws, among other 
ideas occurs that of resistance ; this must therefore be fixed 
once for all, in order that the validity of those laws may have 
a meaning. For iron, according to the investigation which- has 
been carried out, this is a doubtful problem. Over against 
the reflection that, in order to make comparisons with other 
metals possible, the resistance of unmagnetic iron must be 
taken into consideration, stands another, that this quantity is 
inaccessible to experience. Since, then, the laws of Ohm, 
Joule, and Lenz, &c., hold good for it alone, experience, 
which of necessity makes use of the empiric notion of resist- 
ance, must giAe deviations from the laws. 

According to Ohm's law the resistance is independent of 
the electromotiA'e force*. This of course is true also of the 
ideal resistance of an iron ware ; its real resistance must, on the 
contrary, change ichen the electromotive force, and with it the 
current-intensity , is changed. For with the latter the circular 
magnetization, and with this the resistance, increases up to 
the limit of saturation. 

In order to test this requirement experimcntall}^, I made 
use of an arrangement which permitted the electromotive 
force to be varied instantaneously. This was a plug commu- 
tator constructed upon a plan of Professor Meyer's. Upon a 
hardgum plate the brass pieces represented in the shaded part 
of fig. 5 (PI. I.) are fixed. By inserting metal plugs in the conic 
apertures they can be connected by means of the binding- 
screws A, B, &c. with one onother and with the other parts of 
the circuit. If, for example, a galvanic element (the positive 
pole is always first mentioned) be connected Avith E and B, a 
second Avith A and H, a third Avitli G and F, and of the plugs 
only those at a, d, e, and h be fixed, while the binding-scrcAVS 
C and D serve merely for carrying off the current, the three 
elements are inserted one after another. If now the plugs at 
a and h be taken out, and plugs put in at b, c, /, and g, the 
three elements are inserted side by sidef. 

For my purpose I inserted the commutator at A and in 

* Accordiug to the last Report made to the British Association, for 
copper this laAv agrees perfectly, so far as the accuracy of obseiTation ex- 
tends.— 7A'/i/. ii. p. 207 (1878)' 

t Let nie be permitted to take this opportunity to recommend for lec- 
ture-purposes the above-de.-cribed and another commutator, like%vise pro- 
posed by M. Meyer, of -which the drawing fig. 6 is an illustration. A 
combination of uuc specimen oi the Jirst and tico of the secoiut sort makes 
it possible for the lecturer to pass over at pleasure from any gah-anic 
experiment to any other by uierel}' transposing the plugs. M. I'iuzger, 
of this place, supplies them excellently executed. 

the Galmnic Current throiKjli Iron. 219 

one diagonal of the Wheatstone square ; between B and D a 
DanielPs element (in the order of succession copper — zinc) 
was inserted, between F and H two, and between G and E 
three such elements in the same direction and one behind an- 
other. The plug at b was never put in, those at a and h 
always; if beside these there were now fixed in place only 

g and /' c, e, f <', y, d g a-nd d c, e, d e and d 

then there were 

12 3 4 5 6 

elements inserted. 

The double and triple elements can thus be simply excluded; 
the single one can, it is true, be only weakened by the secon- 
dary closing ate; I found, however, that in reality it is thereby 
likewise excluded. 

The resistance in the elements hardly came into considera- 
tion in comparison with that of the rest of the circuit ; the 
intensity of the current therefore varied nearly as the electro- 
motive force. I at first intended to make those experiments 
with the wires already used for the others ; but they exhibited 
a behaviour so abnormal that I was obliged to replace them 
by fresh ones that had not been submitted to galvanic and 
magnetic treatment. I will cite only a few instances of these 
abnormities. Through a thin annealed iron wire (the magne- 
tization-experiments made with which are not included among 
those above selected) the current of 2D was sent, without in- 
termission, for one minute each time, first in one and then in 
the other direction. The following resistances a and b were 

a 14-57 14-42 14-29 14-23 14-14 14-11 14-06 14-06 14-03 
14-32 14-03 14-00 13-98 13-96 13-95 13-94 13-94 

b 13-74 13-37 14-15 13-71 13-38 13-69 13-43 13-81 13-39 
13-82 13-44 13-89 13-44 13-81 13-51 13-79 13-39 

While, therefore, a apart from a gradual diminution, 
amounting to about 4 per cent., connected with the gradual 
lowering of the surrounding temjierature, shows constancy, 
the values of b form a tolerably regular ziozaaf line, the 
maxima of which deviate on the average 3 per cent, of the 
entire ox'dinates. Further, the next day the mean resistance 
(the wire being differently fixed), on the employment of 

ID, u-i = 14-92 


ID, u-i = 14-92 "i .. -1 

2D «- =15-63 1^''^-"'^ = ^^^ 
3D; z4=16-33J ^^'^-^^'2 = 0-^0 

220 Dr. F. Anorbacli on tlte Passatje of 

A\as found to bo 


So colossal an alteration of resistance (almost 5 per cent.) 
could not have escaped the observers, and is moreover in itself 
imj)robable ; it even overpasses the limits of the alterations of 
resistance by magnetizings as above oiven (§ 0). 

A third scries of experiments, tinally, showed that when the 
current passed through cijutinuously the resistance diminished 
enormously; there was, namely : — 

A**™* After Ag-ain, ^ _ ^ . ,» 

A^fi^*- Imiii. after 3, ^' ^' "'^ "^^^^^^tes. 

?f = 16-54 10-23 16-01 15-92 15-83 15-82 (constant). 

The current was then opened for a short time, and again 
closed ; a reiterated diminution of lo was the result ; at 
?r= 15*70 constancy appeared to have come in again; and so 
it went on. All these phenomena may at once be characterized 
as consequences of the disturbed molecular relations of the 

Even with new wires there is one diificulty not unimportant. 
By every alteration of the electromotive force the thermal 
equilibrium of the wire is disturbed, as the radiation for some 
time does not keep pace with the increased heating. In one 
branch of the Ijridge, however, which consists exclusively of 
Gennan silver, the heating has very little, but in the other, in 
which is the iron wire, an important influence. I have en- 
deavoured to approximately determine this influence from the 
numerical data supplied by Weber, Favre, and Bosscha. In 
Bosscha's units the electromotive Ibrce of a Daniell is in round 
numbers 10^\ therefore in Volta's units of current and 
Siemens's resistance-units 10. Now, in operating I constantly 
added only one element (never more) at a time. We shall 
therefore obtain an upper limit for the heating if we calculate 
the heating by 2D; that eftected by ID is not sufHcient, be- 
cause the heating increases as the square of the electromotive 
force at constant resistance. We have thus the electromotive 
force E = 20 ; and the mean of the total resistance of the two 
sides of the tetragon through Avhich the current flowed was 
exactly the same — namely, 10 in the comparison branch (»-2, 
conf. § 3), and 10 on the average in the iron wire. The cur- 
rent-intensity is therefore = 1. At the same time, according 
to Favre, 1-G unit of heat is generated, therefore 0*8 in the 
iron wire. The weight of the latter amounted to at least 
10 X 0-1 X 10000= 10000 milligrams, or 10 grams. These 10 
grams of iron are about as much heated as 1 gram of water 

tliC Galvanic Current tlvroiKjh Iron. 221 

l)y an equal quantity of heat. The rise of temperature thus 
amounts to 0°*8 R. or 1° C. Six seconds were required for the 
determination of the resistance. As, then, a rise of tempera- 
ture of 1° C. augments the resistance 1 by 0*0005, thermal 
influence appears in fact not to be excluded. 

These reflections I first made after having, as I believed, 
already proved, by numerous series of experiments "without 
taking this circumstance into account, the dependence of the 
resistance upon the intensity of the current. Of the results 
of some of those series I will quote the mean values, — first, 
because at least so much can be inferred from them, that even 
after deductino; the thermal alterations of resistance others 
still remain, and, secondly, because the comparison with later 
experiments, which Avere free from thermal influences, fur- 
nishes indeed a confirmation of the calculation we have just 

1. Unannealed iron wire. / = 2120, (7 = 0*28. In the mean 
of symmetrically distributed experiments in sets of 5 each: — 

(ID) u-i = 7-7570, (2D) «-o = 7-7600, (3D) ^-3 = 7-7630: 

u-o -«'i = 0-0030, «-3 - 10-2 = 0-0036. 
Therefore u'n+x — ic^^ is nearly constant, and 

''"^'~"'" =g= +0-00043. 


This number, it is true, is below the extreme value found 
for the effect of the heating ; but the probable value corre- 
sponding in this case to the extreme value of that effect does 
not at any rate amount to more than the half of the former ; 
it therefore amounts to no more than 0-00025. It is there- 
fore established, to a high degree of probabilit}-, that the resist- 
ance increases with the intensity of the current. 

2. Repetition of experiment 1. 

«'^=7-7482, ■?<-o= 7-7526, u"3=7-7574; 
therefore mean of S = 0'00059. 

3. As experiment 2 had given a higher value of S than ex- 
periment 1, so a third series of experiments gave for it a still 
higher value ; for the result was : — 

M-i= 7-7469, zr.2= 7-7528, ii'3= 7-7587; 

S = 0-00076. 

This gradual increase of 8 furnishes a confirmation of what 
was assumed at p. 219, that the high values of S in the wire 
there under investigation might be a consequence of its having 
been several times used galvanically. 

222 Dr. F. Aiicrbach on llie Pa6sayeof 

4. In a thin iron wire, Bunsen elements being employed, 
the following; were Ibund as the means of many experiments, of 
whieh two consecutive ones only were constantly used for the 
formation of the differences of resistance: — 

/r2-(ri = 0-0037, ?r3-«-2 = 0-00411, '^^^^^=0-0041, 

Mean 0-0042; 
(mean of u- = 6-83) therefore 

8 = 0-00061. 

If this 8 were solely a consequence of the heating, it could 
not but be much greater in comparison with the S of experi- 
ment-series 1. 

The results of another series of experiments, in which the 
thermal influences were at most very slight, are graphically 
represented in lig. 7. 

5. The share of the temperature-influences in the value of 
8 was compelled to represent itself isolatedly in a copper wire. 
The copper was pure, /= 18000, f/ = 0-41, and the mean value 
of u' = 4-164. I found, on employing the same Bunseu ele- 
ments as in 4, 

<t.3_«-i = 0-00090, 

^^^^^-8 = 000011. 

This value agrees with the probable value of the thermal 
influence for this special case, so far as agreement is possible 
in rough calculations of this sort. 

Of various artifices which I em})loyed in order to exclude 
the influence of heating, the folIoAving finally proved to be the 
most effectual, at least with thin wires. The resistance of the 
iron wire was determined approximately, to one or two places 
of decimals. On closing the bridge, there then resulted a still 
smaller deflection toward one side, perhaps toward that to 
which corresponds too small a measuring resistance. The last 
ficTure of this measurinfr resistance was then made 1 higher by 
insertion in the resistance-case, so that now, on the closing of 
the bridge, a deflection resulted toward the o]»])Osite side. Let 
these two deflections be equal o,, and h„ for the case in which 
11 elements are used ; if these are small quantities (in the ex- 
periments their angles never exceeded 15'), and ii' induction- 
phenomena of every sort are excluded, any observed deflection 
Sn can be reduced to an additive or subtractive resistance by 
dividing it by a„ + b„, according as this deflection is observed 
fit the taking-out or insertion of a unit in the last place of de- 

tlie Galvanic Current through Iron. 223 

cimals of the measuring resistance. In this way we can get 
with great exactness two more decimal-places ; hence I made 
the experiments as follows: — 

(1) 10 approximately determined; 

(2) Si^f^. . . s„_, 5„s,t_i . . . SgSi observed, and from them a 
system of simultaneous values of Si . . . s„ derived ; 

(3) «! + hi, ffj + h,2- • ' ^n + ^>n obscrved ; 

(4) Experiment 2 repeated inversely — 

This again gives a system of simultaneous deflection-values. 
Finally the mean of these two was taken afresh. It then re- 
presents a system simultaneous with the determinations 3, and 
can by means of them be exactly reduced to a system of ad- 
ditive or subtractive resistances. 

Here the current remained closed, on the average, only a 
few seconds ; so that a thermal influence could hardly assert 
itself (compare below). On the other hand, the extra currents 
in thick Avires made the procedure impossible ; hence I was 
obliged to confine myself to thin ones. 

6. Hard iron wire /lo- / = 24300, (f = 0-21. 1-3 Daniell 
elements. (Preliminary experiment.) 

1(7=103-9 deflections (to the left*): 

5i=0-0, .^2 = 2-3, .^3=4-7, .^2=2-9, .^i-l-2. 

Therefore the simultaneous values are 

5i = 0-6, s2 = 2-6, 6^3=4-7. 

Now there were found 

ai4-Z>i = 4'7, a2 + /^2~^'^> a3 + />3=12-2. 


16.1 = 103-913, w'2 = 103-930, ?r3 = 103-939, 

therefore in the mean 

K'2 — It'i 


:S^2 = 0-00017, 

in fact much less than at p. 

In the following Tables of the results of the exact experi- 
ments, the index in the first column states the number of the 
Daniell elements; the second column gives the sum (a + h) of 
the deflections, left and right, for a unit more or less in the 
last decimal in the approximate statement of ?<; ; s and s' are 
the mean values of the deflections found before and after the 


* "To the left" denotes constantly "to the side corresponding- to a too 
tie measuiino- resistance." 

224 Dr. F. Ancrltncli on llie Pussofje of 

(letorminution of a + h; w and iv' tlic corresponding true resist- 
ances; ;• denotes "right," I "left." 

7. Wire/io. From 1 to 6 Daniell elements. rr=103-i». 




1 s'. 






0-5 r 

0-.3 r 














1-0 ; 

























= Si 2 = 0*00010. 

Of the differences z<;„—it'„_i the tirst are constant — namely, 
10, 9, and 9 respectively; the last two, on the contrary, are 
greater, namely 17 and 16: these latter point to thermal in- 
fluences. These are in general easily recognizable in that 
they increase with n, while the influence in question here must 
diminish with n (on account of the gradual saturation of the 

8. Annealed iron wire/u. ^=43200, d=0-20o, ?y= 182-6. 











6 1 



























i 669 

















The influence of the heating is here still more clearly di- 
stinuuisha])le from that of the intensity of the current. The 
latter gives 

!^±i::!^i=gi ^=0-00019. 

Hence we get 812 = 0-00014. With the hard wire/jo the 
decrease of the quantities ir2 — w'l, u'3 — iCg, &c. was very slow. 
There, at all events, the influence of the current-intensity far 
exceeds 7i = 4. But there Si.j = 0-00028, while 5i2 = 0-06010. 
Therefore t/ie dependence of the resistance on the intensitt/ of the 
current is f/reater there than here; ichUe here Si 2 '*' greater, i. e. 
the dependence is concentrated upon a smaller region. If Ave 
imagine curves constructed for both cases, the abscissse repre- 
senting the current-intensities .r, the ordinates the resistances 

the Galvanic Current through Iron. 


y, both will approach to the horizontal rectilineal form for x 
increasing ; but this right line will possess a larger ordinate 
for hard wires, and commence at a larger abscissa. Compare 
fig. 8. 

9. Repetition of 7. u-= 102-4. 




20 r 
3-3 ^ 

2 9r 


























In all quahtative relations this series agrees with 7. The 
differences decrease very slowly ; from « = 4 they increase, in 
consequence of thermal influences ; only the absolute values 
of the differences are somewhat greater; namely, there becomes 

Si o = 0-00016. 

In order to fix for steel also the curves drawn for hard and 
soft iron, I made experiments with wires of elastic steel. They 
did not, however, in general yield results of corresponding 
trustworthiness. Only thus much could be concluded from 
them, that the ordinate of the straight horizontal line in which 
the resistance-curve with increasing intensity of the current 
ends is much greater than with hard iron, and commences at 
a still greater length of abscissa. I will communicate at least 
one such series of experiments. 

10. Steel wire F^. ^=3500, fZ = 0-43. Approximately 
w = 3'53 (for s) and =3'54 (for s'). 










. 8 

31 1 





i 10 
; 11 

? 4 







































5io = 0-00033. 

But the total alteration is not yet concluded, even at n=6. 

The following last two Tables refer to control-experiments 
with copper wires. In both, for o^s a very small negative 
value came out ; at greater values of n the influence of the 
heatiuo- then asserted itself. 

'^'2i) Dr. F. Auerbacli on the Passajc vj 

11. Wiro of pure copper. /= 18000, r/ = 0-4:l, u- (iipproxi- 
mately) =4*32 and 4-31 respectively. 




s'. 1 w. w'. 1 Mean. 




2 Or 












4-3171 1 4-3106 

68 05 

69 07 
69 07 

71 07 

72 : 08 


— 2 



S^ 2= -0*00005. 


Platinized copper wire. 

/= 15000, (f = 

= 0-12, Zt 

»= 30-15. 




5'. j W. 







0-2 r 





0-2 i 

0-2 r 









+ 3 

+ 12 



g^2= -0 00005. 

I have shown that, when the intensity of" the current rises 
from ID onwards, the resistance also increases ; and with soft 
iron wires we could follow this increase up to its limit. But 
now, how does the resistance change Avhen, starting from ID, 
we let the intensity fall ? That then xl- also declines is indu- 
bitable; but two circumstances, further, ftivom* the conclusion 
that it sinks rapidly, at least in soft iron wires. For, first, we 
have seen that the quantity »"„+,—«•„ diminishes when n in- 
creases, and therefore increases with a falling n ; and there is 
no ground for assuming that the curve changes its law at the 
arbitrary value .i'=lD. And, secondly, the magnetizing- 
expcriments give us direct information respecting the total 
change of resistance with the circular magnetizing, conse- 
quently with the current-intensity ; the negative values of S, 
however, were disproportionately greater than the positive 
values which were here given for 814; the rest must therefore 
arrive at the quantity 8„|. I have tried various methods for 
determining this quantity — that is, for comparing the resist- 
ance of an iron wire when the current is infinitely little with 
the resistance when the current has a finite intensity. They 
have, for the present, all failed, partly at the limit of sensitive- 
ness of the galvanometer, partly at the comparison, which 
could not be carried out, even when the absolute determina- 

tlte Galrcniic Current f/iroiK/h Iron. 'I'll 

tion of «'q had been accomplished. I nevortheless intend to 
continue these trials. 

The preceding considerations disclose to view an interesting 
analogy with some of those in dynamics and thermodynamics, 
which I will briefly express. 

(1) The coeficient of elastic'ity is the ratio of an increment 
of pressure to the lessening of yolume produced. Simultane- 
ously with the latter, however, there results a rise of tempera- 
ture. According as this is balanced or not by any force, e. g. 
by radiation or conduction, we obtain for the coefficient of 
elasticity a less or a greater value. 

(2) Specific heat is the ratio of a quantity of heat to the rise 
of temperature produced. But simultaneously with the latter 
an expansion ensues. According as this is compensated by 
an external pressure or not, we get for the specific heat a less 
or a greater value. 

(3) The resistance of an electrical conductor is the ratio of an 
electromotive force to the current generated. But, if the con- 
ductor is magnetically polarizable, at the same time a circular 
magnetizing residts. According as loe balance this by any ex- 
ternal force {for instance, hy a longitudinal magnetizing) or not, 
ice obtain for the resistance a less or a greater value. 

As the second proposition is reciprocal to the first, so a 
fourth can be placed over against the third ; it does not, how- 
ever, belong here. 

Even Joule's law respecting the heating of the closed cir- 
cuit cannot strictly hold good for iron ; or, more exactly ex- 
pressed, if in Joule's formula 

W= const, rw 

we put, for the heat W developed and for the resistance iv, 
values directly given by observation, we must obtain for the 
constant a value different according to the value of i, but 
always too high in comparison with other metals. Lenz has 
observed the times necessary for equal developments of heat 
with different current-intensities, resistances, and metals; he 
in fact found nearly constant numbers for the product tihc. 
These numbers, however, cannot be quite constant. For the 
theoretic deduction of the law presupposes the absolute con- 
stancy of the quantity ic during the process under considera- 
tion ; but in reality this never takes place, because the resist- 
ance is dependent on the temperature. It is only the electro- 
motive force E that remains constant. Now, since Lenz's 

228 On tlic Passofje of tlie Galrauic Current throuf/h Iron. 
constant can be written in the form 

— J 


it follows that evoiy increase of w i)y the p:issap;e of the cur- 
rent must itself lesson that constant. Indeed Itobinson* has 
eontinned this by showino; that t diminishes with / increasing. 
But in iron, tipart from the heatino-, a i'urther increase of lo 
takes place particularly through the magnetizing. Hence, 
with equal values of i, the constant must come out smaller for 
iron — indeed, since the true value to be taken into account is 




and since, according to the experiments in § 4, — rises to 


1'03, as much as 3 per cent. less. I have given at the com- 
mencement of this memoir (p. 3) the average numbers which 
result from Lenz's experiments. Their ditferences may most 
probably bo attributed to errors of observation and the want 
of accuracy of the method. If, ho^^■ever, we try to bring the 
above reflections into harmony with Lenz's number for iron, 
this can be done perfectly ; for indeed the number for iron is 
the smallest, and about 3 per cent, below the mean of the 
three other numbers. 

The earlier view, that the temperature-coefficient « of the 
resistance of a metallic conductor might be the same for all 
pure metals, has not been verified by experience; i7iter alia, 
the deviations from the mean value 0'0037 are very consider- 
able. Various quantities, too, must have an influence upon 
the value of a — for example, the specific heat, and, just as 
much, also the specific magnetism. As, according to G. 
AViodomannf, the magnetizability increases with the tempera- 
ture, and since, as we have shown, the resistance increases 
with the magnetizing by the current, the resistance of iron 
must increase with the temperature more rapidly than that of 
other metals. The value of « is. according to my data, in the 
moan about 


This value is in fact hioher than the mean value for the rest 

* Trans. Roy. Irish Acad. xxii. (1) p. 8. 

t Togg. A)in. cxxii. p. 4G;Jj Galvanismus (2), ii. (1) p. G04. 

Electro- optic Observations on various Liquids. 22*J 

of the metals, for which (with few exceptions) a lies between 
0-0036 and 0-0038. In the supposition that a part of this dif- 
ference is to be accounted for by the strong niagnetism of iron 
we shall be confirmed when wo consider that (with the excep- 
tion of platinum) the lowest value of a belongs to bismuth, the 
most stronglj diamagnetic metal — nameh', 

a=0-0035. . 

1 have here selected only a few points, which show a rela- 
tion to the question in hand in the most direct and striking 
manner. The reader who is intimate with the theories con- 
cerning it will find in other departments also, e. g. in the 
beautiful investigations of G. Wiedemann on the connexion 
between galvanic currents, torsion, and magnetism, multifa- 
rious points in which a connexion with the foregoing analyses 
is recognizable. 

The carrying-out of my experiments in the laboratory of this 
University has been much furthered by the willing assistance 
of Professor Meyer, for which I here express my gratitude. 

Breslau, 2otli June, 1878. 

XXYI. Electro-optic Observations on vanous Liquids. St/Jo'SN 
Kerr, LL.D., Free Church Training College, Glasgow. 

[Continued from p. 102.] 
31. ~V\7"E come now to the fixed oils. Two of these (olive and 
▼ ' castor) had been already examined carefully in the 
old cell — the former with good effect, the latter not. The fixed 
compensator is now withdrawn: but all the other arrangements 
are as formerly for CS2 (6, 7). The principal difficulty of 
electro-optic experiments on liquids (the obtixiuing of a suffi- 
cientlv clean charo-e) is now much aosravated. Sometimes 
the method of working already described (2) is not perfectly 
adequate, except at the expense of much time. Even when 
every known precaution has been taken, and charge after 
charge of the same oil passed through the cell, there are often 
a few visible specks left in the liquid, either solid particles or 
small bubbles, which interfere materially with the observations. 
But even in such cases, I generally get a pure and regular 
effect bv takino; a line of sight a little above or below the axal 
part of the field. And when the specks are very few, and the 
electro-optic action of the liquid not extremely feeble, the 
regular effect is often obtained at the centre of the field clearly 
enough, though it is always marred more or less by the pre- 
sence of the solid particles or bubbles. 

32. Olive-oU, the purest obtainable from the apothecaries — 
PhU. Mag. S. 5. Vol. 8. No. 48. Sept. 1879. R 

230 Dr. J. Kerr's Electro-ojdu' 

transparent, and a very ^ooJ insulator. As in all the insula- 
ting li(iuid,s yet examined, so liere, electric force restores the 
litrht clearly from pure extinction in the polariscope. The 
ert'ect is a good deal stron^^er than some of those already ob- 
served and certainly characterized. AMien a spark is drawn 
from the prime conductor, the lio;ht restored by electric force 
vanishes at once, thouoh not with such ap])arently ])erfect 
abrujitness as in CS2. When the li<>ht is well and steadily 
restored by electric action, and the hand compensator is ap- 
plied in the usual way, horizontal compression is found to 
strengthen the light in every case, while horizontal tension 
weakens it to pure extinction. The action of olive-oil under 
electric force is therefore contrary to that of CS2 (9), the one 
action being perfectly regular and (to sense) absolutely pure 
as the other. 

33. Oil of Sweet Almonds, the best obtainable I'rom the 
apothecaries — paler, and apparently purer and finer than olive- 
oil, and a very good insulator. The action of this li(|uid under 
electric force in the cell is not distinguishable from that of 
olive-oil, except that it appears rather stronger. Under good 
conditions easily obtained, the neutralization of electric action 
upon almond-oil by horizontal tension of glass is always per- 

34. Oil of Poppy-seed, got in a good colour-shop as prepared 
for the use of artists — colourless, transparent, and a good insu- 
lator. I have never seen a perfectly clean charge of this oil 
in the cell ; but I have obtained a regular effect with it in the 
Avay already described (31). The action of the liquid under 
electric force is similar to that of olive-oil, being always neu- 
tralized perfectly by horizontal tension of glass. I thought 
the effect somewhat fainter than those observed in the olive 
and almond oils. 

35. Oil of Bape-seed. — As obtained from the oil-merchant, 
this licjuid contained a large quantity of sediment. After half 
a dozen filtrations through Swedish paper, the oil was appa- 
rently clean and very clear, and of a faint amber colour. It 
acted in the cell as a moderately good insulator, the sparks 
from the prime conductor being reduced in length about two 
thirds when the connecting wires were ])ut in position (10). 
In electro-optic experiments with this oil I never got a per- 
fectly clean charge of the cell ; but good optical effects were 
obtained with perfect regularity above and below the centre of 
the field. The effects were apparently a little fainter than 
those just observed in poppy-oil : they were e(|ually ])ure, and 
of the same kind, the light restored by electric force from pure 
extinction being strengthened always by horizontal compres- 

Observations on various Liqtciih. 231 

sion of oflass, and weakened always to extinction Lv horizontal 

oG. Oil of Colza. — As obtained from the merchant, this oil 
also contained a large amount of solid sediment. -After several 
tiltrations it was beautifully clear, and of a pale amber colour. 
Tried in the plate cell, it acted as a very good insulator, the 
sparks from the prime conductor being yery little shortened 
when the connecting wires were put in position. In electro- 
optic experiment this oil was one of the cleanest that I had yet 
examined which accounts partly for the fine effects obseryed. 
These were of the same kind (contrary to OS2) as in the pre- 
cedinfj oils, but a oreat deal stronger. For the first time in 
any fixed oil, I now" saw the extinction-bands well deyeloped 
by the hand compensator. They were almost as fine as those 
formerly observed in cumol; and, as Avas to be expected, they 
afforded a good illustration of the difference between the fixed 
oils and the former liquids. It may be remembered that in 
cumol, as in carbon disulphide, the bands are developed and 
moved in towards the axis of the field, against electric force, 
by vertical tension of glass, or by horizontal compression. In 
colza, on the contraiy, the bands are developed and moved in 
towards the axis by horizontal tension; and the action is pure 
and constant here as in cumol. 

37. Oil of Mustard-seed, obtained as " Genuine East India" 
from the apothecaries — transparent, and of a rich yellow colour 
inclinincj to orano-e. Tested in the usual way, it acts as a 
pretty good insulator, the spark-length of the prime conductor 
being reduced not so much as one half when the connecting 
wires are placed. In electro-optic experiments with this oil I 
never got a perfectly clean charge ; but good optical effects 
were easily obtained above and below the centre of the field. 
The effects were pure and perfectly regular, and of the same 
kind (contrary to CS2) as in olive-oil, but apparently fainter. 

38. Raw Linsenl-oH, of a brownish-amber colour, fairly 
transparent, and only a moderately good insulator, the spark- 
length of the prime conductor being reduced by it about three 
fourths. This liquid was extremely troublesome in electro- 
optic experiment, chiefly from the difficulty of cleaning it. 
Not until many successive charges had been filtered and passed 
through the cell did the polariscope give any sure sign ; and 
at the best the effects w^ere obtained only Avell above or below 
the centre of the field. At last, however, the optical effect of 
electric force on this oil was found to be quite certain and 
regular, though extremely faint ; and it was certainly of the 
same kind (contrary to CS2) as in the other oils. A sample 
of refined linseed also was examined, and with similar results, 


232 Dr. J. Kerr's Electro-optic 

31.). jViif-oll. — III the first olcctro-optic i rial tliis oil was very 
dirty; but it <>;ivc ii good rooulur ofiect, Avliich was neutralized 
(as the ett'ec't in olive-oil) by liorizontal tensit)n. After several 
Mltratious and renewals ot cLargc in the cell the oil was very 
little improved, still dirty and hazy, giving a faint diffused 
light even at initial extinction, and showing a heavy chain 
between the electrified balls, as well as dancing particles in the 
outer parts of the field. But amid the confusion thus produced 
the optical effect was obtained regularly and clearly. The 
effect was of the same kind as in olive-oil, but apparently 

40. Lavd-oil. — As obtained from the oil-merchant this was 
merely a thick slush ; but filtration gave a fine clear oil of a 
bright amber colour. Tested in the usual way, it acted as a 
pretty good insulator, the striking-distance of the prime con- 
ductor being reduced by it about one half. As with nut-oil, 
so here, I found that repeated filtrations and renewals of the 
charge made little difference. The oil was never perfectly 
clean: there Avere always a few flickering particles in the outer 
parts of the field, as well as a stationary chain or set of chains 
between the electrified balls. Still the effect of electric force 
was observed regularly and very distinctl}' in the polariscope. 
The effect-was of the same kind (contrary to CS2) as in olive- 
oil, but certainly stronger. The extinction-bands, though not 
in any case well developed, were brought out clearly by hori- 
zontal tension of the hand compensator. 

41. JS'eatsfoot-oil, very like lard from first to last, but a 
purer-looking oil, and clearly stronger as an insulator. Under 
electric force it gave in the polariscope a perfectly regular 
and very good effect, which appeared stronger than that of 
lard. The effect was of the same kind as in all the preceding 
oils, being neutralized perfectly by glass extended in a direc- 
tion parallel to the lines of force. 

42. Sperm-oil. — Two samples were used, the purest that I 
could obtain from the oil merchants. They differed a little in 
colour, the one being a clear amber, and the other paler with 
a tinge of green ; they differed also in insulating-power, the 
striking-distance of the prime conductor being reduced fully 
three fourths by one of them, and only about one half by the 
other. Both samples were examined at some length and with 
great care. Many successive charges were passed through 
the cell, the last of tliem very clean; but even at the best the 
liquid was somewhat hazy, as if from the presence of gelatinous 
matter. One of the samples, the weaker insulator, gave no 
sure trace of effect in the electro-optic ex})eriment. The other 
sample gave an eftect which was undoubtedly real, but too 

Observations 'on various Liquids. 233 

fiiiut to be characterized in the usual way. I therefore applied 
a more delicate method, "which I have sometimes found very 
useful. Working from the best possible extinction, and before 
the electric force "svas applied, 1 introduced the hand compen- 
sator, and applied a very feeble strain steadily, so as to merely 
destroy the purity of initial extinction in one direction or the 
contrary. The electric force was then applied ; and I found re- 
gularly that the effect of horizontal tension was clearly strength- 
ened by electric force, and the effect of horizontal compression 
clearly weakened. These results were obtained consistently 
many times in succession, and with several successive charges; 
but, considering their singularity, I could not be satisfied till 
I had seen them under better conditions. 

43. Purified Sjierm. — Sufficient quantities of the two pre- 
ceding samples were given to Mr. Tatlock, the public analyst 
for Glasgow; and he kindly had them purified for me with 
great care, by a process which is described in ]\Iiller's ' Che- 
mistry.' As the oils left the hands of Mr. Tatlock he consi- 
dered them extremely pure and dry. In electro-optic experi- 
ment there was now no difficulty or doubt about either sample, 
the effects being much stronger than before. By electric force 
the light was well restored from pure extinction; and the effect 
was always neutralized perfectly by horizontal compression of 
glass, and always strengthened by horizontal tension. Judging 
from memory, I thougbt the eft'ect was at least as strong as 
the similar effect observed in Young's light paraffin (29), and 
a great deal stronger than the contrary effect observed in lin- 
seed-oil {o^). One thing is certain, that the action of sperm- 
oil under electric force is of the same kind as that of carbon 
disulphide, and contrary in character to the action of every 
other fixed oil yet examined. 

44. Seal-oil, a transparent but somewhat hazy liquid, of a 
pale amber colour, and a good insulator. In electro-optic ex- 
periment this oil acted as regularly as the others already men- 
tioned, and gave excellent effects, though it was never perfectly 
clean. By electric force the light was restored brightly from 
extinction in the polariscope, and the effect was neutralized 
perfectly (as in olive-oil) by horizontal tension of the baud 
compensator. The extinction-bands were developed clearly, 
though not very strongly. The eft'ects appeared to be the most 
intense that I had yet seen in the fixed oils excepting colza. 

45. Codliver-oil, finest Norwegian, transparent, and of a 
faint greenish colour. In electro-optic experiment this oil 
gave regular and strong effects, which were neuti-alized per- 
fectly (as in olive-oil) by tension of glass in a direction parallel 
to the lines of force. The extinction-bands also were seen 

234 Dr. J. Kerr's Electro-optic 

Elementary Measurements. 

4(3. The only new piece introduced is a Thomson's long- 
range electrometer. My particular instrument is the second 
that Mr. White has constructed of the kind, and it is modelled 
closely on the tirst. For a full descri[)tion and a good figure 
of this electrometer, I must refer to 8ir AV. Thomson's reprint 
of Papers on Electrostatics and Magnetism. The unit of 
scale-value of potential which 1 ado})tis one turn of the screw; 
the whole range of the instrument is 200 ; and the highest 
potential ordinarily sustainable in the prime conductor of my 
plate-machine is about 180. 

lln-ee guarded wires are led from the prime conductor, one 
to the fij-st outer ball of the plate-cell (the second outer ball 
being always connected with earth), another to the inductric 
plate of the electrometer, and the third to the knob of a 
small condensing-jar, whose outer coating is connected with 
earth. The use of the condenser is to slacken and regulate 
the rate of variation of the potential. The pieces and con- 
necting wires are placed properly, so as to leave the action of 
the electrometer undisturbed. The rest of the arrangements 
are precisely as in the experiment of extinction-bands (11), 
and as exhibited in the diagram of (3. 

47. Method of Observation. — Tlie plane of polarization of 
the light rendered by the first Nicol being always at 45° to 
the lines of force or to the horizon, and the second Nicol being 
fixed at extinction, a weight of one or more pounds is attached 
to one of the jilates of the fixed compensator, so as to give a 
definite initial restoration in the ])olarisco])e. Two observers 
attach themselves, one to the electrometer and the other to the 
polariscope; and the machine is w'orked at a proper rate, under 
direction from the first observer, so as to give a slow but steady 
rise of potential. The second observer watches for the first 
appearance of the patch of light at the centre of the black axal 
band (11), and he marks the instant of its appearance by a 
sharp signal. The first observer sees whetlier the index of 
the electrometer is beyond the sighted position or short of 
it at the instant of the signal, and he works the screw ac- 
cordingly. The observation is repeated several times if ne- 
cessary, the screw of the electrometer being properly worked 
each time until the index is in the sighted position at the 
insta7it of the sifjnal : and the scale-readincj of the electro- 
meter is then recorded as the measure of the potential which 
neutralizes the definite birefringent action introduced at start- 
ing. Two other scide-readings are generally recorded at the 

Observations on various Liquids. 


same time, one giving an observed lower limit of potential, 
and the other an observed higher limit : these are determined 
in the same way as the preceding, the index being clearly 
beyond the sighted position in the one case at the instant of 
the signal, and clearly short of it in the other case, always with 
rising potential. 

Although the details of this method were adopted as the 
best that occurred to me in the course of a good deal of pre- 
liminary work, the final observations were not quite satisfac- 
tory. The effect in the polariscope varied in many cases so 
slowly that the observed limits of potential were too far apart. 
The compensator itself was subject to small irregularities, which 
it was almost impossible to prevent or to neutralize perfectly. 
Whether these difficulties are inseparable or not from the 
method, and how far they might be overcome by a good 
choice of materials and by very careful work, I am not yet 
able to judge. 

48. Carbon Disnlpliide. — The following Table contains the 
results of two early sets of observations. Columns A and B 
give the numbers of pounds attached to the first and second 
plates respectively of the fixed compensator ; column C gives 
the observed range of corresponding or sensibly neutralizing 
potential ; D and E the observed lower and higher limits of 
potential ; G the potential as inferred from the ]ireceding 
numbers. Column K gives the observed increments of poten- 
tial corresponding to a constant increment of birefringent 
action (2 pounds on second plate). 



















86, 87 





113, 115 





136, 138 





151, 154 












91, 92 












124, 128 












163, 164 




The next Table contains an unaltered record of the most o f 
my last day's work with CSa.' All the conditions of observa- 
tion Avere kept as constant as possible. The columns are de- 
signated exactly as in the former Table, 


Dr. J. Kerr's .Electro-optic 



1 *^" 

! ^- 





5o, 59 
























'.Xi, 98 







89, 90 





103, 105 

87 J 






95, 98 











• 2 

104, 107 



































125, 128 





130, 137 







130, 131 





13(>, 139 







132, 136 





140, 143 










49. I proceed to draw several inferences, beginning -with 
an extension of the statement already made in 9. 

(1) Throughout the range of these observations, the optical 
eftects manifested are sensibly pure cases of double refrac- 
tion ; the plate of carbon disulphide acts, under electric force, 
as a positive imiaxal Avitli axis parallel to the lines of force. 
This is evident from the nature of the arrangements, and from 
the constantly observed fact that, as the potential rises through 
a proper range of value, the light at the centre of the field 
passes through sensibly })ure extinction. 

(2) The total weight on the iixed com])ensator may be 
adopted as a good approximate measure of the corresjionding 
birefringent action. The three following lines of numbers are 
taken from the second Table. The first line gives the total 
Aveights attached to the fixed compensator ; the second gives 
the observed values of the neutralizing potential Avhen the 
whole weight is attached to the first phite ; the third gives 
the observed values of the potential when the weight is dis- 
tributed between the two plates, 2 pounds always on the second 

G 7 8 9 10 11 

1051 114 Un 12Gi 130i 134 
104" 114 120" 125 13U 136^ 

From these results, and others of the same kind, I infer that, 
■within the present range of measurement, the Aveight and the 










Observations on various Liquids. 237 

optical effect are sensibly proportional^ and each approximately 
a measure of the other. 

(3) As the potential increases, the intensity of the corre- 
sponding bireiringent action also increases. This is evident 
from both Tables. 

(4) The increments of potential corresponding to a constant 
increment of birefringent action have sensibly smaller values 
at high than at low ])otentials. This is distinctly proved by 
column K of both Tables. It shows that the intensity of the 
optical effect varies more rapidly than the potential. Any 
conclusion more definite would be perhaps premature at pre- 
sent, and until the numerical results are more consistent ; but 
the following is not without interest. 

(5) "Working from a fair average of the best measurements, 
putting V and r' for the scale-values of potential correspond- 
ing to two consecutive birefringent actions g and ^ + 1 (mea- 
sured by integer pounds of tension), and determining n suc- 
cessively so as to satisfy a set of equations of the form 



_ ^ + 1 

^ \ _ 

\r / q 

I find that the intensity of the optical effect varies more 
rapidly than the second power of the potential through the 
whole range of observation, but not more rapidly than the 
third poAver except for low potentials. Between birefringent 
actions 1 and 2, the value of n is slightly in excess of the 
number 3. The average value of n for all the observations is 
almost exactly equal to |. 

50. Measurements in other Liquids. — The method of obser- 
vation has been already described in detail (47). The num- 
bers in the first line of the following Table give the pounds of 
tension in the fixed compensator ; those in the second line give 
the scale-values of the neutralizing potential in CSj; and so 
forward for the other liquids named. " 

12 3 4 

Carbon disulphide 57 69 80 90 

Cumol 81 971 111 122 

Carbon dichloride 115 ... 161 

Xvlol 115 137 160 

Tohiol ■] 

Cymol )- 130± 160 + 

Benzol J 

Amylene 145 + 

Terebene 180 + 

Benzol {hix) 105 147 176 

238 Dr. J. Koit".s EUdru-optlc 

The numbers for the first three liquids are probably exact ; 
those for xylol and the following liquids are doubtful, though 
certainly not far from the truth. It is worthy of notice that 
the potentials for carbon dichloride are to the ojjtically oqui- 
volent ])otentiaIs for carbon disulj)hid(; almost exactly as 2 
to 1. The corresponding ratios for cuinol as compared with 
carbon ilisulphide are also very nearly equal to each othei", 
their values being 1-41, 1*41, 1'38, 1"35. AVe infer that opti- 
cally equivalent potentials in carbon disulphide, cumol, carbon 
dichloride are very nearly as the numbers 10, 14, 20. The 
last line of numbers contains the results of a particular ex})e- 
riment (a])})arently a very accurate one) with benzol, in 
which the arrangements were so made that the restoration in 
the polariscope was in the form of a star or bright iVinge on 
the contour of the })Ositive ball. By a comparison of the 
numbers with those above them, it will be seen how great are 
the variations that may be induced in the optical effect by a 
small change of conditions, and how great is the care that 
must be taken to secure any thing like consistency of results 
in this line of work. 

Optical Effect of Electric Discharge through NitrohenzoL 
51. Experiment. — The diagram shows all the pieces in ho- 
rizontal section through the source of light L and the obser- 
ver's eye E. 

J^ B 


V^. -^ 


Earth ^j* 

The cell D F is charged with nitrobenzol; and its outer balls 
D and F are connected by wires, one with the prime conduc- 
tor and the other with earth. One of the wires is interrupted 
by an air-interval about half an inch long, limited by t\yo brass 
balls A and B, which are supported upon movable ])illars of 
varnished glass. The light from a i)arattin flame L passes 
through a horizontal slit (about an eighth inch wide) in a 
screen P Q, then through the first Nicol M, which is fixed 
with its principal section at 45° to the horizon, then through 
the plate of nitroben/.ol, then through the second Nicol N. 
The object seen in the polariscoi)e is a narrow and very well 
outlined luminous oblong, lying along the axis of the electric 
field, and extending nearlv from ball to ball. 

Observations on various Liquids. 239 

Tilings being thus prepared, the second Nicol is turned to 
pure extinction, and the machine is set in motion. At the 
instant of each spark through A B, and then only, there is a 
clear instantaneous reappearance of the luminous oblong iu 
the polariscope. As the interval A B is shortened while the 
machine is worked at a constant rate, the optical effect becomes 
fainter by degrees till it disappears, which it does before the 
air-interval is reduced to zero. The facts are exactly simihir 
to those observed already in 24. 

52. I have repeated this experiment with several variations; 
and I shall now mention the principal results. 

(1) As long as the plate- machine is used, there is one 
thing found to be essential in all forms of the experiment : 
the discharging train from prime conductor through cell to 
earth must be interrupted by an air-interval (an insulating- 
shell) A B of some length. The optical etfect is observed at 
the instant of the spark through A B, and at that instant only. 
The position of the interval A B appears to be of no conse- 
quence ; it may be before or after the cell, near earth, near 
cell, or near prime conductor. Mere discharge is not suffi- 
cient. Spark-discharge through a very short air-interval is, as 
we have already seen, without sensible eflect ; so also is glow- 
discharge, brush-discharge, and even crackling spark-discharge 
from the shaft of the insulated ball F upon the observer's 
knuckle or upon an earth-connected ball. 

(2) When the prime conductor is connected with the knob 
of a small Leyden jar whose outer coating is connected with 
earth, the optical eliect obtained as in 51 is very much in- 
tensified. And when the discharges through the liquid are 
obtained from a powerful Holtz (two 20-inch [)lates) which is 
provided with the usual condensers, the effect becomes still 
more brilliant. These observations agree with that already 
made (in 51) in connexion with the shortening of the in- 
terval A B. 

(3) When the two Holtz conductors were connected with 
the outer balls D and F of the cell, the sparks through the air- 
interval A B in one of the connecting-wires became extremely 
dense and strong as A B was lengthened ; and now, for the 
first time in my observations, the purity of the restoration in 
the polariscope was in some degree lost, the old object (though 
seen clearly enough) being displaced and distorted irre- 

(4) Not even with the torrents of electricity rendered by 
this powerful machine when worked at the hardest, did the 
continuous discharge (air-interval zero) give any sensible 
effect from pure extinction in the polariscope. 

240 Di-. J. K('ri".< J'Jlcctro-oj'tic 

(5) AVlien a laroc iiulnction-ooil workod bv one Grove's 
element was nsed as a source of electricity, 1 ioiuul it sufH- 
cient to connect the balls D and F with the two ends ol" the 
coil by unbroken wires. The lioht was then sustained coiiti- 
mialiy troni initial extinction in the |)olarisco[)e, but always 
Avith a -Nery sensible flicker. The liquid required in this case 
to be particularly clean ; for otherwise the effect was marred 
by specks or chains of particles, as in the former experiments 
with insulatino- liquids when these were not very clean. 

(6) The contrast between the central and the outer parts of 
the field, with reference to intensity of optical effect, is as 
marked here as in any of the insulating liquids. Returning 
to the experiment of 51, I remove the screen P Q and turn 
the flame L edgewise to the cell, so that the object in the 
polariscope is a narrow vertical streak of light extending well 
above and below the balls. The object now restored in the 
polariscope by dischargii is a comparatively short central seg- 
ment of the flame, lying well Avithin the cylinder which enve- 
lops the two balls, and fading gradually to extinction at both 
ends, but very well outlined lateially. 

53. Experiment. — The arrangements and procedure of 51 
are retained with only one change ; the ])lane of polarization 
of the light rendered by the first Nicol is horizontal or vertical — 
that is, either parallel or perjiendicular to the line of discharge 
through the centre of the cell. The optical effect of discharge 
in the polariscope is now evanescent. 

In most of my repetitions of this experiment, the restoration 
from pure extinction was reduced to an extremely faint but 
still perce])tible Hash at the instant of each spark ; but when 
the cell was placed at a good distance from the eye, and great 
care was taken otherwise Avitli the observation, this faint effect 
disap])eared completely. The Nicols had only to be turned 
then through half a right angle each, to give the strong and 
clear effects already described in 51. These observations 
were made with the longest s[)ark from the plate machine. 

54. Special Eyepiece. — Many attempts were made to sup- 
plement the information obtained in the last article, by bring- 
ing the nitrobenzol-effect into closer comparison with the 
effects formerly observed in CSg and other insulating liquids. 
The results given by the hand compensator pointed certainly 
to one conclusion ; but they were not very distinct, nor were 
they even regular enough to be satisfactory until recourse was 
had to a special eyepiece. 

This is a small })iece made of brass, and shaped somewhat 
like a common thread-bobbin with the shank prolonged a little 
way through one of the flanges, this flange being grooved as 

Observations on various Liquids. 241 

a pulley. A very acute prism of flint-glass is laid flat upon 
the fiice of the other flange, and is attached rigidly to the 
bobbin by a screw cap, so that a ray of light, received along 
the axis of the tubular shank, enters the prism normally as it 
leaves the tube, and is then deviated through a small angle by 
refraction. The bobbin has its shank supported in proper 
bearings fixed at the edge of a whirling table, and can be made 
to revolve round its geometrical axis very rapidly. When a 
point is viewed through the bobbin by an eye placed close 
behind the prism, the rotation of the bobbin transforms the 
luminous point into a fine and faintly luminous circular line. 
With my particular prism, this ring of light is rather too large 
to be "well commanded as a whole by the observer's eye ; but a 
good view may always bo had of as much as half the circum- 
ference. There is of course a little dispersion ; but this is of 
no consequence. 

55. Arrangements. — These are the same as in 51, with a 
few additions. All the optical pieces are shown in the adjacent 


: / 


K X 


The flame L is turned broadside on to the cell; and the 
horizontal slit in the screen P Q is reduced to a very small 
Avidth. The lens G is so placed as to give a real image of the 
slit at the centre of the cell, the image being a narrow and bril- 
liantband, lying along the axis of the electric field, and extending 
from ball to ball. The second lens H assists the observer's vision. 
S is the special eyepiece (54), carefully placed beforehand so 
that the axis of the shank, which is also the axis of rotation, 
coincides with the line of the ray L MN. The piece K,between 
cell and analyzer, is a square plate of glass a quarter of an inch 
thick, which ispermanently strained in a small screw press, the 
line of compression being parallel to the faces of the plate. 
The use of K is the same as that of the hand compensator ; but 
its action is more uniform, and can be made very much 

As in 51, the first Nicol M is fixed with its principal 
section at 45° to the horizon, and (the plate K being away) 
the second Nicol is fixed at extinction. 

242 t)r. J. Kerr's Electro-optic 

Let tlic plate K be now put in position as in the diafrrani, 
with the line of coinpi"('s.><ion either vertical or horizontal. 
The light is restorcil in the jiolariseojx', and ajipears (when 
the eyepiece S is at rest) as a sharply (lefincd and very narrow 
horizontal band extending- from ball to ball ; but when the 
eyepiece is set in motion, the band is transformed into a large 
ring, narrow and bright at the top and bottom, wide and faintly 
luminous at the sides. The plate K is finally removed ; and 
the extinction is seen to be pure. 

5G. J'lvperlment. — Things l)eing thus prepared, the cell is 
charged with clean Jiitrobenzol, and the balls D and F are 
connected with the terminals of a large Euhmkoi'tfs coil by 
unbroken wires. The coil is worked by one GroA^e's element, 
and gives a half-inch spark with broken circuit. 

(1) The eyepiece S is left at rest. When the currents 
pass, the luminous band is restored continually in the polari- 
scope, not, however, as a steady light, but flickering or 
quivering very rapidly. For our present purpose, this is a 
much better form of effect than any thing that can be obtained 
from the plate machine. 

(2) The eyepiece S is set in motion at a moderate speed. 
When the currents pass, the light is restored in detached 
bands, which are distributed, of course, as generating elements 
of the luminous ring observed immediately above (55). No 
trace of the ring can be detected except the flashing bands 
themselves, these being separated by wide and perfectly dark 

(3 ) Observation (2) is carried forward, the eyepiece being 
now driven round as rapidly as possible. There is a clear 
change of optical effect, the bands restored by the currents 
being enlarged into wide patches, which are much fainter in 
their later than in their earlier parts. It ajipears thus that 
each of the discharges of the coil through the liquid, considered 
as a discharge o])tically eftective, occupies a sensible interval 
of time ; it appears also that each discharge falls gradually in 
power towards its termination. There was nothing like this 
widening of the l)ands observed with the plate machine in any 
case, with or without condenser. 

(4) The plate K is compressed, so as to give much the 
same eti'ect in the polariscope as the hand compensator when 
well strained ; and it is then put in position with the line of 
compression vertical (55). When the currents jiass, and the 
eyepiece revolves at a moderate rate, the flashing bands are 
well restored on the faintly luminous ground of the ring ; and 
when the eyepiece is driven veiy rapidly, the bands are widened 
as in (3). The flashes are quite as distinct to the eye as in 

Observations on various Liquids. ^24:6 

observations (2) and (3), though thoy are not now on a dark 

(5) Observation (4) is carried forward, with only one change : 
the plate K is laid with the line of compression horizontal. 
There is an evident change of optical effect. The flashing 
bands are fainter ; and when the eyepiece revolves as rapidly 
as possible, the bands are not widened nearly so much as in (4). 
The optical effect of discharge appears thus to be weakened by 
horizontal compression. 

(0) The compression of the plate K is increased by degrees, 
and the observations (4) and (5) are repeated at intervals. 
The contrast between the two cases comes out more and more 
strongly, till at last, when the compression has reached a 
certain value (a value greater than could have been antici- 
pated) , the contrariety is manifestly perfect. When the line 
of compression is vertical, the flashing bands are sensibly as 
distinct as ever ; but when the line of compression is hori- 
zontal, they are evanescent and, under good conditions, quite 

(7) When the right degree of compression has been reached 
by trial as in (6), the observer takes the piece K in his hands, 
and turns it rapidly round the ray, backwards and forwards 
through a right angle, the eyepiece revolving and the currents 
passing all the time. The effects are brought out thus in a very 
striking form, and are seen to be perfectly regular and decisive. 

An intense electric current through nitrobenzol is therefore 
optically equivalent to tension along the line of discharge, or 
to compression in the perpendicular direction. 


57. The principal results will now be summed up briefly. 

(1) When an insulating liquid is traversed by electrostatic 
force, it exerts a purely birefringent action upon transmitted 
light. In relation to this action, liquids are divisible into 
two classes, the positive and the negative. 

(2) Positive liquids act as glass extended in a direction 
parallel to the lines of electric force, or as plates of quartz or 
other positive uniaxals with axes parallel to the lines of force. 
Carbon disulphide is the best exampte. 

(3) Negative liquids act as glass compressed in a direction 
parallel to the lines of force, or as plates of Iceland spar or 
other negative uniaxals with axes parallel to the lines of force. 
Oil of colza is one of the best examples. 

(4) In the following Table the positive liquids are arranged 
as nearly as possible in the descending order of electro-optic 
power, the larger and clearer intervals being marked by sepa- 


Dr. J. Kerr's Electro-optic 

rating linos. Tho nogative liquids aro not so arranged ; but 
colza and seal oils arc certainly among the strongest, and 
linseed is the weakest. 

Positive Tjiquid^. 
Carbon disulpbide. 


Paraffin-oil (sp. gr. -890). 

Carbon dicbloride. 






Paraffin-oil (sp. gr. '814 ). 




Nesrative Liquids. 
Fixed oils of vegetable oritiin: — 


Sweet almonds, 



Rape-seed , 



Fixed oils of animal origin : — 





Valeric acid ? 

The birefringent actions of these twenty-six dielectrics 
have been observed repeatedly ; they are perfectly regular, 
and, to sense, perfectly pure. Valeric acid alone is so faint as 
to be doubtful. 

(5) All the negative liquids yet known belong to the class 
of the fixed oils. Sperm-oil holds an exceptional place, being 
clearly positive. 

(G) The infiuenco of density on electro-optic power is 
marked and certain in tho case of the paraffin oils, increase of 
density being accompanied by increase of electro-oj)tic power. 

(7) In carbon disulphide and several other liquids, electro- 
optic measurements are manageable through long ranges of 
potential and optical effect. Tho results of some careful 
trials in this direction are given in 4i( and 50. 

(8) Stannic chloride exerts a very strong optical action 
under electrostatic force ; but the character of the effect is 
not yet certainly known (27). 

(9) Of the forty or more liquids yet examined in the plate 
cell, there are none that exhibit any moderate degree of 
insulating ])ower except the twenty-seven now named in 
(4), (8). This appears to justify the generality of the state- 
ment made in (1). 

Observations on various Liquids. 245 

(10) When nitrobenzol is traversed by an intense electric 
current, it exerts a purely birefringent action on transmitted 
light. The action is similar to that of a positive uniaxal plate 
with axis parallel to the line of discharge. 

58. In conclusion I shall give several reasons for preferring 
liquid dielectrics to solids in electro-optic experiment. 

Liquids are free from temper and irregular strains ; and, 
if we except some such bodies as oil of turpentine, they 
are of themselves quite inactive in the polariscope. Solids, on 
the contrary, such as moderately thick plates of glass, are 
almost in every case irregularly active of themselves when 
inserted between two crossed Nicols. This difference is of 
much consequence when the work is delicate. 

The optical effects of electric force are more complex in 
solids than in liquids, being partly due to electric force at 
the point or points viewed, and partly due to mechanical re- 
actions of distant and differently strained parts of the body. 
I think it extremely probable that the remarkable phenomena 
lately observed by Mr. Gordon in plates of glass were due to 
these mechanical reactions. 

Liquid dielectrics are not permanently damaged in any 
degree when they are traversed by disruptive discharge, while 
solids in such a case are rendered useless. And to see the 
practical importance of this difference, it should be noticed, 
first, that the preparation of a solid for accurate examination 
in electro-optic experiment is always a matter of some expense 
and trouble, and, secondli/, that we cannot submit any dielectric 
thoroughly to such examination without running the risk of 
electric discharge through its mass. 

When a plate cell has heeW carefully constructed once 
for all, any number of liquids may be examined in it succes- 
sively, each liquid (if only clean enough) adapting itself 
perfectly to all the conditions of the experiment. Solid 
dielectrics, on the contrary, have to be drilled and mounted 
individually ; and this (as already said) is always a matter 
of expense and trouble. 

The plate cell affords a geometrically constant field for any 
number of dielectrics in succession, which is a matter of 
capital importance in all comparative observations and mea- 

For the reasons now indicated, and notwithstanding the 
strength of glass and some other solids as dielectrics, I think 
it probable that liquid dielectrics will supersede solids 
altogether in this line of experiment. 

PJiil. Mag. S. 5. Vol. 8. No. 48. Sept. 1870. S 

[ 24G ] 

XXVII. On the Construction and Use of a Scale for Gna(jhi<i 
Ci/lindrical Meastircs of Caparitij. Bij Sir (r. B. AiRY, 
K.C.D., Astronomer lioijal* . 

SEVERAL years ago, when I was officially engaged on the 
national measures, I arranged a simple scale for rapidly 
guaging the cylindrical measures of capacity which are sanc- 
tioned l)y law, and which are in fact the only measures in 
ordinary use. I understand that this scale is now sometimes 
eni] loved for its proposed pur])OSC. 1 do not rcmemher that 
the principle of its construction has heen published; and I think 
that there may be advantage in making it known. 

The cubical capacity of a cylinder, whose axial depth in 
inches is called " depth," and whose diameter in inches is called 
"diameter," is = depth x (diameter)- x -785398. As the 
cubical capacity of the gallon is 277"2738 cubic inches, that 
of the half-gill (the smallest of our measures), or -^^ of the 
gallon, is 4'o32-403 cubic inches. Hence we have for the half- 


depthi X (diameteri)2x •785398 = 4-332403, 

or depthi X (diameteri)'^ = 5-516 19. 

As the cubical capacities of our measures (half-gill, gill, half- 
pint, pint, quart, half-gallon, gallon, peck, half-bushel, bushel) 
proceed in continued binary progression, we have 

for gill, depths X (diameter2)^ = 2 x 5*51019; 

for half-pint; depthg x (diameter3)- = 4 x 5-51(319; 
and so on, the factors of 5-51619 being the successive powers 
of 2. 

Taking the logarithms of both sides, 
log depthi + 2 X log diameteri = -74164, 
log depths + 2 X log diameters = -74164 -h -30103, 
log depths + 2 X log diameters = -74164 -h 2 x -30103, 
log depths + 2 X log diameter4= -741G4 + 3 x -30103 ; 

and so on, the numbers on the second side increasing in arith- 
metical progression, with the common difference -30103. We 
are at liberty to multiply these equations by any arbitrary 

number; and wc shall adopt the multiplier -Trrr-./Vo7v/v> or 

^ ^ -oOlOoOO 

33*21928. And we shall add to both sides the number 

Thus wc find, foi. half-giU, 

33-219 X log depth: + 66*439 x log diameteri- 14-6368 = 10 ; 
* Couinuinicated bv the Author. 

On a Scale for Giiaging Cylindrical Measures of Capacity. 247 

for gill, 
33-219X logdepth2 + (36-4o9x log diameterg- 14-0368 = 20; 

for half-pint, 
33-219 X log depths + 68-439 x logdiaineter3-14-6368 = 30; 
and so on, the right-hand number rising to 100 for the bushel. 
It will be remembered that the logarithms are common loga- 
rithms corresponding to the number of inches in the depth 
and in the diameter. 

The number —14-6368 may be divided into two parts, 
— a and —h, subject only to the condition that a + &= 14-6568. 
And as we propose to use two engraved series of numbers, 
one relating to the depth and the other relating to the dia- 
meter, we may attach —a to the first and —h to the second; 
so that the numbers of the first column will be 
33*219 X log (depth in inches) —a, 
and those of the second column will be 

66-439 X log (diameter in inches) —h. 
And we have now to consider the details of the two engraved 
series which will represent these. 

When we plunge the material scale into the cylinder, to 
touch its bottom, we obtain, in inch-measure on the scale, the 
cpiantity of " depth." But the engraved numeral is to give 

"(33-219 X log depth) -a," 
or "(33-219 x log inch-measure) —a." 


" 33-219 X log inch-measure " = " engraved numeral + a ;" 

^^^^ //I . 1 ,, engraved numeral + a 
'logmen-measure = — oo.oia » 

and, taking the exponentials of both sides, 

" inch-measure " = -, , , 

. II- engraved numeral +a 

number whose log is — ~ .^ .^ , , , . , 

^ oo"Zlv 

— number whose log is -030103 x (engraved numeral + a). 
In like manner it is found for the scale which is applied to 
the diameter, 

" inch-measure " = 
number whose log is -0150515 x (engraved numeral +1). 
By these formulae the measures are given corresponding to 
every engraved numeral. 

It will be remarked that the succession of engraved lines on 
these scales differs strikingly from that on the common loga- 
rithmic scale. With equal intervals of numerals, the intervals of 
engraved lines on the scale become larger with increasing num- 
bers. The scales may properly be termed " exponential scales." 
On referring to the investigation, it will be seen that, if the 


248 Sir G. B. Airy on (he Const met ion and Use of a 

doptli of u evlinJcr bo nieasiirecl by the engniveJ numerals on 
the depth-scale, and the diameter by the engraved numerals 
on the diameter-scale, the sum of the measures ^vill be 10 for 
half-gill, 20 for gill, m for half-pint, 40 for pint, kc. 

As the zero-end of the scale is always to be brought to con- 
tract "Nvith the bottom or with the interior of the circle, that 
end ought to ])e hard ; in other respects the scale may be a 
very light rod. If the bottom of the measure is spherical, the 
measure of depth to be adopted is the mean of those taken ; 
one Avith the zero-end of the scale resting on the centre, and 
the other close to the circumference. 

The following numbers have been computed for the gra- 
duations of the scales — using for a, 2*321, and for Z>, 12'315. 

Measures, in Inches, for the Graduations of the Scale for 


in inches. 


in inches. 


in inches. 


in inches. 























, 37-6 
































■ 380 

























16 701 
































































17 653 















39 3 















































































































15-262 I 








15-368 , 























Scale for Guagwg Cylindrical Measures of Capacity. 249 

Measures, in Inches, for the Graduations of the Scale for 




n inches.' 


ui inches. 


in inches. 


m inches. 




11-127 ' 
























11 360 
























11-599 1 














6 570 


























12-008 i 








12091 j 








12-175 1 








12-260 , 




2 668 


7-417 i 


























































12-959 1 






































































9 787 













































































































And the rule for measuring the capacity of a cylinder, so 
far as to ascertain whether it an-rees with the leo;al measures 
in ordinary use, is as follows : — 

Measure the depth with the scale marked " deptli " and take 
the reading. 

Measure the diameter with the scale marked " diameter " 
and take the reading. 

250 Mr. (J. (J. Hutchiuson on a cont-enicnt Source 
Add together the two readings. The sum will be :- 
For halC-gill IQ-O 

„ gill 20-0 

„ half-pint 30-0 

„ pint 40-0 

„ quart 500 

„ half- gallon CO-O 

„ gallon 70-0 

„ pock 80-0 

„ half-bushel 90-0 

„ bushel „ 100-0 

XXVIII. On a convenient Source of Ileal for Chemical Ope- 
rations. Bij CiiKiSTorHER Clauke Hutchinson, Af^soc. 
E.C.ScJ. 4r* 

OST chemical laboratory operations require some source 
of heat, Avhich should be capable of being readily a}j- 
plied and varied to meet the requirements of each individual 

This is effected, in most instances, by the combustion of 
coal-gas in an ordinary Bunsen burner. Circumstances may, 
however, debar the operator from the use of coal-gas. He 
may be called upon to carry out some process, e. g. in the 
workings of a mine, at the side of a mineral spring, in the 
collection of water, gas, or air, in field blowpipe woi'k, kc, or 
finally, his laboratory may have to be hastily improvised in a 
country district (especially in a partially civilized country) 
where coal-gas is not obtainable. 

He has then to fall back upon the older and more crude 
methods, such as the spirit-lamj), the wind- Or charcoal-fur- 
nace, etc., which are at the best incovenient, and often fail to 
give satisfactory results in their employment. None of them 
can be readily varied according to the desired temperature ; 
and they require some dexterous manipulation, or a consider- 
able amount of attention. 

To supply this want, a simido method suggested itself to 
me which I ])elieve maybe of utility under some of the condi- 
tions above enumerated. It will be found efficient as Avell as 
sim})le, the cost both for material and apparatus 1)eing smnll, 
in addition to which it can be rendered exceedingly port- 

It is Avell known that many of the common forms of the 
liquid hydrocarbons are easily vaporizable, even at the ordi- 

* Commiuiicated bv the Author. 

af Heat for Chemical Operations. 251 

nary temperature. Mixed with the amount of air necessary 
for their complete combustion, it occurred to me, their vapours 
would form an efficient substitute for coal-gas. This method 
I have tried, and found to yield excellent results. 

The vaporization is effected bypassing a brisk current of air 
through a column of the liquid, sufficient being vaporized to 
yield an exceedingly efficient combustible mixture. 

The apparatus used is exceedingly simple and of trifling 
cost, the liquid hydrocarbons used being either common me- 
thylated ether, benzol, naphtha, or common alcohol. The 
mixture of the benzol hydrocarbons, almost universally sold 
and known as " henzoline,'''' is preferable, on account of its 
small cost and its higher volatility. 

A moderately tall and rather narrow cylinder (like those 
used in the Wanklyn process of water- analysis, or even a large 
test- or boiling-tube) is fitted with a good cork, through which 
pass two tubes analogous to those of an ordinary Avash- 
bottle : one passes to the bottom of the cylinder and serves as 
an ingress-tube for the current of air, the other (just entering 
through the cork) serving for an egress-tube. The cylinder 
being almost filled with the volatile liquid, a brisk current of 
air is passed through, and the air, saturated with vapour, led 
off from the egress-tube to an ordinary Bunsen burner, Avhere 
a steady and intensely hot flame is obtained. By regulating 
the current of air or vapour by means of a tap, the flame can 
be varied with the same facility as that of an ordinary gas- 

The current of air may be maintained by means of a large 
gas-holder, a reversible aspirator like that used by Dr. Angus- 
Smith, or even a foot-bellows. By fitting up a large test-tube 
in the manner described, and by using a small foot-bellows, 
an exceedingly portable apparatus is obtained. For the supply 
of a small laboi'atory where a number of lights are required, 
the apparatus can be varied with equal facility and at very 
trifling expense. The vaporizing-cylinder may be replaced by 
a metallic vessel, or a tall, somewhat narrow bottle ; and a con- 
tinuous and powerful supply of air can be maintained from the 
apparatus described by P. Casamajor* in the 'American 
Chemist.' This apparatus, being Avorked by the supply of 
water from one of the service Avater-taps, needs scarcely any 
attention; and thus a continuous supply of combustible vapour 
can be maintained. The egress-tube from the cylinder must 
be furnished Avith branch pipes or T-pieces, as an ordinary 

The combustion of these vapours, it Avill be observed^ gives 
* ' Americau Clieinist/ \o\. iv, p, 3C1, 

252 Notices respecting Nexo Books. 

even a liiglicr l('iiij)erature tlian that of eoal-gas ; they also 
jjossess the advantage of yielding pure and innocuous combus- 
tion products — water and carbonic anhydride. They can 
therefore be employed without danger in the vicinity of deli- 
cate instruments, which would be otherwise injured by the 
acid combustion-products of our impure gas supplies. All 
who are in the habit of using platinum vessels are aware of 
the injurious effect produced upon their surfaces submitted to 
the action of the flame of impure gas : with the use of these 
flames this effect is obviated, and delicate platinum surfaces 
and instruments can be heated or cleansed in them without 

Ex]HMiments made to determine the cost for the supply of 
an ordinary Bunsen-flame gave the consumption of common 
ether about 1*5 ounce per hour, the cost of which is about two 
pence ; with common benzoline the consumption was at the 
rate of one ounce per hour, or under one farthing. 

In tropical climates, such as that of India, where the great 
volatility of ether or benzoline would be unfavourable to their 
use, they might be replaced by naphtha or common alcohol. 
Filling the vaporizing-cylinder with naphtha and immersing 
in water at about 120° F., an intensely hot flame was main- 
tained from the resulting yapour. With alcohol the same 
result followed when immersed in water at about 130° F. In 
those countries where the operator is deprived of the use of 
coal-gas this method for obtaining a supply of heat could be 
used with advantage. 

The experiments were made in the laboratory of the Koyal 
College of Science, under Professor Galloway. 

XXIX. Notices respecting New Boohs. 

The Art of Scicntijic Discover}!, cr the general conditions and 
methods of research in Physics and Chentistry. By G. Gobe, 
LL.D., F.R.S. London : Longmans, Green, and Co. 1S78. 
(Crown Svo, pp. 648.) 
^piIlS is the work of a well-known chemist, of one who has 
-'- practised the art of discovery, and who might be expected to 
discourse well on an art in which he has obtained a certain measure 
of distinction. Nor is the book b}"" any means devoid of interest ; 
indeed, a partial reviewer miglit easily point to many well written 
and instructive passages, he might allege that the book is a store- 
house of facts, that its contents show not only that the author is 
well acquainted with some branches of science, but also that he 
has read the history and at least paid attention to the philosophy 
of science. And yet, while recogniziug the truth of all this, we 
must confess that we have read the book with great disappointment ; 
it seems to us to raise expectations ^hich it by no means fulfils, 

Notices respecting New Boohs. 253 

and suggests comparisons ^vhic•ll are very damaging. While reading 
it, we involuntarily call to mind the "Discourse on the Study ot" 
^Natural Philosophy," and how, in the one, every thing is clear and 
the scope and purpose of the whole plain, while in the other it is 
hard to see the object the author has in view, and the parts, though 
often interestiug when considered as fragments, are apt to have 
no manifest bearmg on the matter in hand. 

The book is on the Art of Scientific Discovery ; and, of course, 
the question arises whether there be such an art. One way of 
answering the question would be to allege that there is an art of 
discovei-y in much the same sense that there is an art of war, or 
an art of poetry — that it is possible to explain the methods by 
which particular discoveries were made, to analyze the evidence 
which is sufficient to distinguish ascertained truth from hypothesis, 
to put in order, and render easy of acquisition, the positive know- 
ledge hitherto acquired, to indicate some of the directions in which 
those who seek are likely to find new truths, but that where an 
ad\ance is to be made the matter must be left to the patience and 
sagacity of the well-informed inquirer. The question has, of 
course, been answered in other ways. Lord Bacon hoped that his 
method, which, however, he never completely expounded, would 
do a great deal more : — " Our method of scientific investigation is 
such as to leave little to strength and keenness of intellect, and 
to reduce all understandings nearly to a level. When it is required 
that a line be drawn straight or a circle round, much depends on 
the steadiness and practice of the hand, if it is to be done by the 
unassisted hand, but little, or nothu^g, if a ruler is used, or a 
pair of compasses : our method is just like this '' (Xov. Org. i. 
(51). This seems quite plain as to what Lord Bacon hoped for ; 
but it is certain that his expectation has not been fulfilled. AVe, 
however, are concerned here with Dr. Gore's opinion ; but we find 
it hard to say what that is. AVe learn that "the late Mr. Faraday 
expressed "' a " favourable opinion of my proposition of framing an 
art of scientific discovery;'' so that one would have thought that 
his expectation resembled Bacon's ; but on the same page we learn 
that he has not forgotten, and apparently allo\AS the justice of, 
Dr. AN'hewell's " assertion that, speaking with strictness, an art 
of discovery is not possible, " and that he has no wish " even to 
suggest the idea of reducing all intellects to a level.'' His " purpose 
is only to show that an art of scientific discovery is much more 
possible than it was in the time of Lord Bacon" (pp. vii, viii). 
Dr. Gore's notion, then, appears to be that to form an art of dis- 
covery is not possible, yet it is more possible than it was formerly ; 
and meanwhile he has undertaken to write " about it, and about it.'' 
This indeterminateness as to the purpose of the book characterizes 
its parts. Let the reader take for instance Chap, xxviii., "Circum- 
stances and occupations favourable to scientific research," and ask 
himself what is the point that the author wishes to establish : we 
doubt whether he will be able to answer the question. The circum- 
stances referred to, taken in order, we should enumerate thus : — 
Professions ; wealth or poverty ; education ; encouragement at the 

254 Notices respecting New Books. 

hands of goverument; suitability of epoch; synipatliy of others ; 
persecution; employment as teacher, lecturer, or examiner; acting 
as assistant to other investigators ; age ; marriage ; connexion with 
scientiHc societies, and "international encouragement." It is 
plain tliat many of these circumstances may be unfavourable as 
well as favourable to scientific research ; and that is how Dr. Gore 
treats them ; but putting that on one side, we can scarcely be 
wrong in supposing that these " circumstances '' were treated of 
just as they occurred to him. There is no apparent attempt at 
classification, and no reason why the list should not be made longer : 
c.y. why not inelude amongst the " circumstances " the character 
of the philosopher's father, or of his mother, whether he was an 
only child or had brothers and sisters, whether he was a teetotaller 
or given to wine and strong drinks, and so on ? The fact is that 
there is no end to such a list ; every circumstance of a man's life 
may be looked at in such a May as to suggest the question, Is it 
favourable to scientific research? But there are only a few cir- 
cumstances in which this point of view is not very artificial; and 
those few Dr. Gore has neither singled out nor discussed. A 
cai'eful and discriminating account of the influence exercised by 
such " circumstances " as encouragement at the hands of Govern- 
ment, connexion with a scientific society, or acti\'e employment as 
a teacher, would have been instructive and pertinent; and this he 
has hardly attempted. But when it comes to the influence of 
marriage on scientific research, the Mrong question is raised. In 
most cases, it is true, a man can only support a wife and family 
by spending all his strength on his profession ; and, of course, 
absorption in a laborious profession is inconsistent with scientific 
research. In these cases, marriage is simply incompatible \\\\h. 
research. If, however, we suppose this in-gent necessity not to 
exist, the question is then, not what the influence of marriage, but 
what the influence of the woman married will be. If the philo- 
sopher, for example, marries X, she will do her best to keep him 
to his crucibles ; but if Y, she will make him frequent kettledrums 
and other scenes of laborious amusement. The influence of marriage 
on research, it would seem, cannot be discussed without a previous 
classification of the characters of women; and this, it is needless 
to say, Dr. Gore does not attempt. To tell us that Lady Hamilton 
helped her husband to \vrite out his lectiu-es (p. 28i»), that Mrs. 
Elaxman was very miu-h annoyed with Sir Joshua Reynolds for 
telling her husband that by marriage he was ruined for an artist 
(p. 281), throws little light on the subject, not much more than 
comes from the luminous fact that twenty thousand men and 
women went to see Buifon buried (p. 2G3). Oddly enough, too, 
Dr. Gore groups his examples as if on purpose to show that men 
become active in scientific research inde|)endently of these " cir- 
cumstances :" thus, some eminent men of science have been rich, 
others poor; souie have been well educated, others the reverse; 
some have enjoyed the patronage of their sovereign, which others 
have been entirely without, aud so on. The only thing that can 
be said appears to be that extreme poverty, absolute want of edu- 

Notices respectmy New Books. 255 

cation, total absorption in a laborious profession, are obstacles not 
to be overcome ; but as this is quite plain to begin with, the whole 
discussion is singularly wanting in purpose. 

It is sometimes curious to notice the irrelevancy of the details 
of Dr. Gore's illustrations ; thus a propos of poor men becoming 
eminent for research, he mentions Hunter, who began life as an 
apprentice to a cabinet-maker, in which capacity he, naturally 
enough, " constructed chairs and tables" (p. 2G3). He after\^•ards 
went into surgery and made the famous collection of anatomical 
prepax-ations. His case aifords a strildng instance of genius and 
industry overcoming obstacles, and proves conclusively that poverty 
in youth is not inconsistent wit]i a life devoted to scientidc re- 
search. Dr. Gore's way of telling the story is tliis : — "With the 
proceeds of his practice as a sui'geon, he bought all the bodies of 
the wild beasts that died in the Tower of London, and of every 
other such animal as he could procure, and dissected them ; he 
compared the anatomy of them all, and discovered the history of 
their organs. In this way he expended more than <£70,000 in 
money, besides immense labour. He was in the habit of swallo\\- 
ing thirty drops of laudanum before delivering each lecture. He 
died at the age of 80 ; and after his death the Englisli Government 
gave =£15,0U0 for his collection of about 20,000 anatomical pre- 
parations" (p. 2G4). This might be an illustration of the fact 
that poverty in youth is not inconsistent with the expenditure of 
large sums of money in middle life ; but the curious point is the 
"thirty drops of laudanum:" the fact is interesting, but utterly 
irrelevant ; for Dr. Gore has not the least intention of showing 
that taking narcotics is a circumstance fa^■ourable to scientific re- 
search. jS'or is this a solitary instance : on the preceding page 
(263) the facts about Linnjeus are nearly all irrelevant. That 
Linnjeus was not stroug, but lived to the age of 71 years, that his 
collection of plants and insects was sold after his death for =£1000, 
and that the King of Sweden sent a ship of war in chase of the 
shij) that was taking it to England are facts which have nothing 
to do with the matter in hand ; but Dr. Gore happened to know 
them, and so wrote them down. We had marked several other 
passages for comment ; but we have perhaps written enough to 
show that the disappointment produced by the perusal of the book 
was not without reasoii, and to justify our opinion that, in spite of 
his possessing several qualilications for the task, Dr. Gore has 
thrown little or no light on the Art of Discovery. 

Wheatstoiie's Scientific Papers. Published by the Physical Society 
of London, 1870. 

The Physical Society of London is to be thanked for having 
undertaken, and to be congratidated for having brought to so 
successful an issue, the republication, in a collected form, of Sir 
Charles Wheatstone's published researches. 

A^^leatstoue's contributions to Physical Science need not be 
looked at through the same glass which is used to magnify the 
merits of many so-called scientific publications. He does not seem 

256 InielU<jcnce and Miscellaneous Articles. 

to liave written unless he had some discovery of his own \o an- 
uouuce. [Such aunouucenients were made in hinp;uage, if not always 
the most polished, yet certainly, to scientific minds, the most 
pleasing, because the most simple. On looking through his papers 
here collected, it seems that almost all his discoveries were crucial. 

lie was essentially witty, if by wit is meant uimbleness in cor- 
relating divers impressions. By viewing an idea from various 
sides and combining those views, he produced a discovery, a solid 

He never wrote for the sake of writing ; nor did he regard 
physics as the application of mathematics to hypothetical matter. 
His mind was in unison with Nature. He seemed to feel that 
theorizatiou should be the servant, not the master, of investigation ; 
and hence his superiority in usefulness over most of his contem- 

The publication of this collection of memoirs by the Physical 
Society, in addition to its own ' Proceedings,' shows, as did the 
publication of Prof. Everett's C.Gr.S. system of physical data, that 
the energies of the Society are well directed. It is to be hoped 
that the scattered memoirs of many another physicist may be col- 
lected and published by the same means. 

XXX. Intelligence and Miscellaneous Articles, 


TT is known that previously to CErsted's experiment it was in vain 
■*- attempted to connect magnetism with static electricity. Xow- 
a-days we can be certain that such a relation really exists, and we 
can formulate the law of it even before making the experiment. A 
magnet in motion exerts at a distance a mechanical action upon a 
body at rest charged with free electricity. This action strictly 
results from the existence of the inverse phenomenon, which has 
been established by the experiments of Mr. l^ow laud*. 

It will be remembered that Eowland showed experimentally that 
the motion of an electrized body acts on the magnetized needle as 
a current would : the direction of the action changes with the sign 
of the electric charge ; and the action due to a given displacement 
of electricity is the same as if that displacement had taken place 
under the form of a current properlv so called. Such are the results 
obtained by Mr. Eowland. On this ground I say that Mr. Eow- 
land's phenomenon is necessarily reversible, and that its reversi- 
bility is a consequence of the impossibility of perpetual motion. 

In fact, if we displace an electrized body so that each point in it 
describes a closed trajectory n times, resuming every time the same 
velocity at the same point, a magnetized needle near it is submitted 
daring the movement to periodically variable forces, in virtue of 
Eowlaud's effect ; this needle can therefore move under the action 
of those forces, and furnish a quantity of work which differs from 

* Helmholtz, Bed. Bcricht. 1870 {Jounial de rhi/s. t. vi. p. 29) ; Phil. 
Mag. [5] vol. ii. p. 23.3. 

Intelligence and Miscellaneous Articles. 257 

zero, although it takes up agaiu at each period its initial position. 
The work is not nil, because the forces producing it depend at each 
instaut on the velocity of the electrized body, and not merely on its 
position. Therefore the magnetized needle furnishes a finite quan- 
tity of work, which becomes intinite with the number of the periods. 
Besides as the system travels along a closed cycle, this work is de- 
rived entirely from the forces which maintain the motion of the 
electrized body. That body is therefore itself submitted to resistant 
forces, which depend on the velocity of the magnetized needle. It 
is the existence of these last forces that we wish to demonstrate. 
If Eowland's effect is the analogue and as it were the complement 
of the phenomenon discovered by (Ersted, the invei'se phenomenon 
here signalized corresponds in the same manner to induction. It 
is even found that moving a magnetic field produces, upon a small 
body charged with a unit of electricity, a mechanical force equal in 
amount and direction to the electromotive force at the same place ; 
only we have here not an electromotive force without action on the 
masses, but a force properly so called. 

From the preceding a curious consequence may be deduced ; it 
is, that static electricity possesses a proper mechanical inertia, 
which is simply added to that of the electrized body. If, indeed, 
an electrized body is in motion in a space where there is no mag- 
net, this motion gives rise to a magnetic field, since a magnetic 
needle in its vicinity would be deflected. The intensity of the 
magnetic field is proportional to the velocity; and consequently 
the variation of that intensity is proportional to the acceleration 
of the body. Now, from what we have seen above, the variation 
of a magnetic field produces upon an electrized point a mechanical 
force equal to the electromotive force of induction, consequently 
proportional to the velocitv of the magnetic variation, and there- 
fore to the acceleration of the body, and with the same direction as 
the acceleration. But a mec}ianical force directed thus, and propor- 
tional to the acceleration, constitutes what is called a force of inertia. 

The ratio of the force to the acceleration is a constant quantity 
for the same electric charge, but not simply proportional to the 
quantity of electricity. — Comptes Rendiis de V Academie des Sciences, 
July 21, 1879, t. Ixxxix. pp. 151-153. 


With the aid of a toothed wheel working against a disk of metal 
or pasteboard, Savart * found that two impulses can make upon the 
ear the impression of a comparable tone ; M. E. Exner t finds by 
means of tuning-forks vibrating before spherical resonators that 17 
impulses, M. Pfauudler i again, by experiments on holed sirens and 
rellection-tones, that only two impulses are required : lastly, M. 
Auerbach§, nearly in accordance with -NI. Exner, that about 20 vibra- 

* Ann. de Chim. et PJn/s. xliv. p. 348 (1830). 

t PHiiger's ArcJiiv, xiii. p. 2:?8 (187G). 

I Tflen. Ber. Ixxvi. p. 572 (1877); cf. A. Seebecb, Pogg. Ajin. liii. 
p. 417 (1S41). § Wied. Ann. vi. p. 591 (1870). 

258 Intelligence and Miscellaneous Articles. 

tions are nocossary for the production of a toiio in the ])hysiological 
sense, the tone being determined to within the interval lOU : Jol. 

Less sharply defined tones can be produced, in an extremely simple 
manner, by only t\AO impulses. AVe have only to put two fingers 
of the hand together so that the ends of the nails are level, and then 
strike somewhat obliquely on a table, for instance, whose proper 
tone is as much deadened as possible by putting books upon it, a 
closed chest of draw ers, &c., eventually moreover by firmly support- 
ing our own body upon it. We shall readily feel, in our hand, that 
the two fingers but rarely strike it simultaneously : and with a 
little attention we always hear (best when the stroke is repeated 
from twice to three times in a second), together with the noise 
(undetermined as to height) of the knocking, a very hollow tone 
and of a height w hich changes ^)fr saltum according to the position 
of the fingers, but which by practice we can approximately have at 
our command, similar tones are obtained by running the finger- 
nail over short lengths of ribbed paper. 

That real tones are heard on knocking can most easily be per- 
ceived from the fact that, on knocking twice with the indicated 
diiierence of time, one can almost always state the interval of the 
tones, and indeed can imitate them (most easily in a whisper), if it 
approximates to one of the musical intervals to which we are 
accustomed. I have often heard with certainty differences of height 
of tone to within about a semitone. The tones from only two 
impulses are therefore determined with certainty to within the mter- 
val 15 : 16. 

If we strike with only one finger-nail, these tones are entirely 
lost ; hence we can easily learn to hear by this if the knocking 
takes place alternately with one and with two fingers. From 
another side also their presence and the correct determination of 
the heights and internal of the tones was confii-med to me. 

Now^ the employment of resonators shows indeed that in the 
noise produced by one knocking on wood, pasteboard, or metal disks 
whose proper tones are deadened, almost all heights of tone are 
represented, but so feebly that, in presence of the distinctness of 
our tones, a resonance in itself unlikely of the objects struck 
may be unnoticed during the period of the observed tone in ques- 
tion. AVith a perfectly quiet surrounding, the tones produced by 
the faintest knocking on stone walls and other heavy solid objects 
can be heard, in which materials such an aftervibration in conse- 
quence of the two feeble shocks, and consequently an objection 
against the assertion that the tones are rendered perceptible by 
only two impulses, is certainly excluded. — AViedemann's Annalen, 
1879, Xo. G, vol. vii. pp. 335, 330. 


The author has made experiments for the purpose of measuring 

Intelligence and Miscellaneous Articles. 259 

directly, by meaus of a spriug dynamometer, the work required for 
the induction of an electric current of determined strength in a 
circuit of given resistance, and comparing it with that Calculated 
from theory. 

A magnetoelecti*ical machine for continuous currents served for 
the induction-apparatus, the electromotive force of which had 
previously been exactly ascertained and found to be proportional 
to the number of turns. The dynamometer was a dynamometric 
winch of the newest consti'uction, provided with a markiug- 
apparatus for sketching the work-curves. Its scale was tested by 
direct loading, and found accurate. The dynamometric winch was 
screwed to the induction apparatus on an axle att:iched to the 
machinery instead of the ordinary which. 

For the measurement of the induced currents a tangent-compass, 
the reduction-factor of which -^as exactly ascertained, was inserted 
in the circuit, of which the resistance was measured as accurately 
as possible, and could be altered at pleasure by means of inserted 
scales. For counting the number of turns a seconds' pendulum 
with a loud stroke was used. 

Five experiments were made : in three the velocity of rotation 
amounted to 1 revolution of the \^inch in 1 second (corresponding 
to 7 revolutions of the inductor) ; in the two other experiments 1 
turn of the winch took 2 and 4 seconds respectively. In each 
experiment 65 turns were executed — once with interrupted, and 
once with closed circuit. The difference between the work recorded 
by the d}TQamometer in the one case and in tlie other was the 
work of induction expended for the production of the current 
simultaneously measured on the tangent-compass according to the 
proportion of the electromotive force calculated from the number 
of turns or from the known resistance. It amounted, according 
to the very well accordant results of the five experiments, in which 
the expenditure of induction-work lay between the limits of -i- and 
6 meter-kilograms, to the electromotive force of one Daniell element, 
and to the resistance of one Siemens unit, reduced 0'13 meti'e- 
kilogram per second — a residt which comes very near theoretical 

Comparing this value of the v»ork \^ ith the number of calories 
corresponding to the chemical processes that take place in a Daniell 
series with equal resistance, we get for the mechanical equivalent 
of the heat, on using the numbers given by W. Thomson and 
Jenkin, the number 428, or, if we take as the basis of the cal- 
culation the higher amount of induction-work in the first four ex- 
periments, the number 421, very closely agreeing with the generally 
accepted equivalent of Joule. — Kaiserliche Alcademie der Wissea- 
schaften in Wien, matJiematiscJi-natrinrissenscJiaftliche Classe, July 3, 
1879. _____ 


The paper contains a criticism of the evaporation theory of 
Osborne Reynolds and the emission theory of Zollner. 

260 Intelligence and Miscellaneous Articles. 

Were evaporation or the emission of molecules on the irradiateil 
side of the vane the only or at least the chief eau.s-> of the radiometer- 
motion, this would of necessity increase when the rarefaction is 
continued, since according to experience both evaporation and the 
emission of molecules must be so much the more vigorous the 
lower the pressure in the space occupied by rarefied gas. But, as 
we have learned from experiments by Fiukener and Crooks, the 
moment of rotation exerted by the flame upon the radiometer at 
first increases, cceti'ris j^nriltus, with the rarefaction of the gases, 
reaches its maximum at a certain pressure, and with further rare- 
faction (h'creaiii's. This diminution of the radiometric effect, which 
may fall to j^^ of the maximum value, contradicts the abo\e- 
mentioned consequence of the theories of evaporation and emission. 
On the other hand, however, the hypothesis that all bodies, in- 
dependently of their aggregate-condition, evaporate even at 
ordinary temperatures cannot be called in question ; hence it must 
be admitted that a force of reaction will also result from the 
emission of molecules. But, in order to explain the above-mentioned 
diminution of the radiometric motion, it must be assumed, further, 
that the reaction-forces resulting from the emission must be either 
vanishingly small, or so small in comparison with the forces arising 
from the recoil of the molecules of the gaseous material still present 
that the motion-phenomena are either exclusively or chiefly con- 
ditioned by the latter forces. 

On this hypothesis, that decrease of the motion can be ex- 
plained, according to the kinetic theory of gases, in the following 
manner : — At the full atmospheric pressure the reaction-force 
called forth on the irradiated side of the vane is too little to o\er- 
come the resistance presented by friction and the air. At sufficient 
rarefaction the reaction-force overcomes those resistances, and the 
motion of the Aane commences. If the reactio'i-force, like the in- 
ternal friction, decreases only verv slowly with the pressiu-e, the 
velocity of the movement attains its maximum at a certain pressure, 
and decreases when the rarefaction is continued, because not merely 
the resistance of the air, but also the force of the reaction excited 
becomes less with the lessened number of the recoiling molecules. 
In a space absolutely void of air the motion must cease entirely, 
if no emission of molecules results on the irradiated side of the 

Further, the author describes a radiometer consisting of a fixed 
cross of mica lamella^ blackened on one side, and a Acry thin 
cylindrical glass case. The distance of the outermost edges of the 
vanes from the glass amounted to 2 millims. "When light fell 
upon it the glass cylinder rotated in the opposite direction to that 
in \\hich the cross would have been caused to turn. 

The object of this experiment is, to furnish a complete demon- 
stration that the motions in the radiometer cannot be explained by 
means of currents of air. — Sitzun// der mathcmat'isch-natanvissen- 
schaftlichen Classe der laiserlichen Ahademie der Wisscnschaften in 
Wien, Julv 3, 1879. 







OCTOBER 1879. 

XXXI. Investigations in Oleics, icith sjyecial reference to the 
Spectroscope. By Lord Rayleigh, F.R.S* 

[Plate VII.] 

§ 1. Resolving, or Separating, Power of Optical Instruments. 

ACCORDING- to the principles of common optics, there is 
no limit to resolving-power, nor any reason why an 
object, sufficiently well lighted, should be better seen with a 
large telescope than with a small one. In order to explain 
the peculiar advantage of large instruments, it is necessary to 
discard what may be looked upon as the fundamental principle 
of common optics, viz. the assumed infinitesimal character of 
the wave-length of light. It is probably for this reason that 
the subject of the present section is so little understood out- 
side the circles of practical astronomers and mathematical 

It is a simple consequence of Huyghens"s principle, that the 
direction of a beam of limited width is to a certain extent in- 
definite. Consider the case of parallel light incident perpen- 
dicularly upon an infinite screen, in which is cut a circular 
aperture. According to the principle, the various points of 
the aperture may be regarded as secondary sources emitting 
synchronous vibrations. In the direction of original propa- 
gation the secondary vibrations are all in the same phase, and 
hence the intensity is as great as possible. In other direc- 

* Communicated by tlie Author. 
Fhil. Mag. S. 5. Vol. 8. No. 49. Oct. 1879. T 

2()2 Lord Riiyleigh's Investigations in Optics. 

tions tho intensity is less; but there will be no sensible dis- 
crepancy of i»base, and tberefore no sensible diniinntion of 
intensity, until tlu> obli(|aitv is such that the (greatest) pro- 
jection of the diameter of the aperture upon the direction in 
question amounts to a sensible fraction of the wave-length of 
tho light. So long as the extreme difference of phase is less 
than a quarter of a period, the resultant cannot differ much 
from the maximum; and thus there is little to choose between 
directions making with the princi})al direction less angles than 
that expressed in circular measure by dividing the quarter 
Avave-length by the diameter of the aperture. Direct antago- 
nism of phase connnences when the projection amounts to half 
a wave-length. When the projection is twice as great, the 
phases range over a complete period, and it might be supposed 
at first sight that the secondary waves would neutralize one 
another. In consequence, however, of the preponderance of 
the middle parts of the aperture, complete neutralization does 
not occur until a higher obliquity is reached. 

This indefiuiteness of direction is sometimes said to be due 
to " diffraction " by the edge of the aperture — a mode of ex- 
pression which I think misleading. From the point of view 
of the wave-theory, it is not the indefiniteness that requires 
explanation, but rather the smallness of its amount. 

If the circular beam be received upon a perfect lens, an 
image is formed in the focal plane, in which directions are 
represented by points. The image accordingly consists of a 
central disk of light, surrounded by luminous rings of rapidly 
diminishing brightness. It was under this form that the 
problem was originally investigated by Airy*. The angular 
radius 6 of the central disk is given by 

<'=l-21«^4 (1) 

in which \ represents the wave-length of light, and 2R the 
(diameter of the) aperture. 

In estimating theoretically the resolving-power of a tele- 
scope on a double star, we have to consider the illumination of 
the field due to the superposition of the two independent 
images. If the angular interval between tho components of 
the star were equal to 20, the central disks would be just in 
contact. Under these conditions there can bo no doubt that 
the star would appear to be fairly resolved, since the bright- 
ness of the external ring-systems is too small to produce any 

* Camb. Phil. Trans. 18;i4. 





Lord RayleigVs Investigations in Optics. 263 

material confusion, unless indeed the components are of very 
unequal magnitude. 

The diminution of star-disks with increasing aperture was 
observed by W. Herschel ; and in 1823 Frauenhofer formu- 
lated the law of inverse proportionality. In investigations 
extending over a long series of years, the advantage of a large 
aperture in separating the components of close double stars 
Avas fully examined by Dawes*. In a few instances it hap- 
pened -that a small companion was obscured by the first bright 
luminous ring in the image of a powerful neighbour. A di- 
minution of aperture had then the effect of bringing the smaller 
star into a more favourable position for detection ; but in 
general the advantage of increased aperture was very appa- 
rent even when attended by considerable aberration. 

The resolving-power of telescopes was investigated also by 
Foucaultf, who employed a scale of equal bright and dark 
alternate parts : it was found to be proportional to the aper- 
ture and independent of the focal length. In telescopes of the 
best construction the performance is not sensibly prejudiced 
by outstanding aberration, and the limit imposed by the finite- 
ness of the waves of light is practically reached. VerdetJ has 
compared Foucault's results with theory, and has drawn the 
conclusion that the radius of the visible part of the image of 
a luminous point was nearly equal to the half of the radius of 
the first dark ring. 

Near the margin of the theoretical central disk the illumi- 
nation is relatively very small, and consequently the observed 
diameter of a star-disk is sensibly less than that indicated in 
equation (1), how much less depending in some measure upon 
the brightness of the star. That bright stars give h.rger disks 
than faint stars is well known to practical observers. 

With a high power, say 100 for each inch of aperture, the 
sharpness of an image given by a telescope is necessariiy de- 
teriorated, the apparent breadth of a point of light being at 
least 8|- minutes. In this case the etfective aperture of the 
eye is -^00 hich. In his paper on the limit of microscopic 
vision§, Helmholtz has shown that the aperture of the eye 
cannot be much contracted without impairing definition — from 
which it follovv's that the limit of the resolving-power of tele- 
scopes is attained with a very moderate magnification, pro- 
bably about 20 for each inch in the aperture of the object-glass 
or mirror. 

* Mem. Astron. Soc. vol. xxxv. 

t Ann, de VObserv. de Paris, t. v. 1858. 

X Lemons d'Opttqne Physique, t. i. p. .309. 

§ Pogg. Ann. Jubelbaud 1874. 

2G4 Lord l^yloigli'.s Imestigations in Optics. 

Vio liavo .scon tlmt a certain width of boam is necessary to 
oljtain a ^ivcn resolvinfr-powcr ; but it does not follow that the 
whole of an available area of aperture ought to be used in order 
to get the best result. As the obliquity to the principal direc- 
tion increases, the first antagonism of })hase which sets in is 
between secondary waves issuing from marginal ])arts of the 
aperture ; and thus the operation of the central parts is to retard 
the formation of the first dark ring. This unfavourable influ- 
ence of the central rays upon resolving-powcr was well known 
to Herschel, who was in the habit of blocking them off by a 
cardboard stop. The image due to an annular aperture was 
calculated by Airy ; and his results showed the contraction of 
the central disk and the aufjmented bri<Thtness of the surround- 
ing rings*. More recently this subject has been ably treated 
by M. Ch. Andref, who has especially considered the case in 
which the diameter of the central stop is half the full aperture. 
How far it would be advantageous to carry the operation of 
blocking out the central rays would doubtless depend upon the 
nature of the object under examination. Near the limit of the 
power of an instrument a variety of stops ought to be tried. 
Possibly the best rays to block out are those not quite at the 
centre (see § 2). 

The fact that the action of the central rays may be disad- 
vantageous shows that in the case of full aperture the best 
effect is not necessarily obtained Avhen all the secondary waves 
arrive in the same phase at the focal point. If by a retarda- 
tion of half a wave-length the phase of any particular ray is 
reversed, the result is of the same character as if that ray were 
stopped. Hence an exactly parabolic figure is not certainly 
the best for mirrors. 

The character of the image of a luminous line cannot be 
immediately deduced from that of a luminous point. It 
has, however, been investigated by M. Andre, who finds that 
the first minimum of illumination occurs at a somewhat lower 
obliquity than in the case of a point. A double line is there- 
fore probably more easily resolvable than a double j^oijit ; but 
the difference is not great In the case of a line the minima 
are not absolute zeros of illumination. 

§ 2. JRectangxdar Sections. 

The diftraction phenomena presented by beams of rectan- 
gular section- are simpler in theory than Avhen the section is 
circular ; and they have a practical application in the spectro- 

* See also Astron. Mouth. Notices, xxxiii. 1872. 

t "Etude de la DiflVactiou daus les lustnuneuts d'Optique," Ann. de 
VEcole Norm. v. 187C. 

Lord Rayleigh's Investigations in Optics. 26o 

scope, when the beam is hmited by prisms or gratings rather 
than by the object-glasses of the telescopes. 

Supposing, for convenience, that the sides of the rectangle 
are horizontal and vertical, let the horizontal aperture be « and 
the vertical aperture be h. As in § 1, there will be no direct 
antagonism among the phases of the secondary waves issuing 
in an oblique horizontal direction, until the obliquity is such 
that the projection of the horizontal aperture a is equal to \\. 
At an obliquity twice as great the phases range over a com- 
plete period; and, since all j) arts of the horizontal aperture have 
an equal importance, there is in this direction a complete rib- 
sence of illumination. In like manner, a zero of illumination 
occurs in every horizontal direction upon which the projection 
of a amounts to an exact multiple of \. 

The complete solution of the present problem, applicable to 
all obhque directions, is given in Airy's ' Tracts,' 4th edition, 
p. 316, and in Verdet's Lecom, t. i. p. 265. If the focal length 
of the lens which receives the beam be /, the illumination V 
at a point in the focal plane whose horizontal and vertical co- 
ordinates (measured from the focal point) are |, -q, is given by 

T2_ ^ V \t n\ 

XY' xY 

the intensity of the incident light being unity. Tlie image is 
traversed by straight vertical and horizontal lines of darkness, 
whose equations are respectively 

sm--^ = 0, sm^ = {^) 

The calculation of the image due to a luminous line (of 
uniform intensity) is facilitated in the present case by the 
fact that the law of distribution of brightness, as one coordi- 
nate varies, is independent of the value of the other coordinate. 
Thus the distribution of brightness in the image of a vertical 
line is given by 

lMrj=^^^^, .... (3) 



2 /2 


the same law as obtains for a luminous point when horizontal 
directions are alone considered. It follows from (3) that in 
the spectroscope the definition is independent of the vertical 


Lord Riiyleigh's Investigations in Optics. 

In order to obtain a more precise idea of the character of the 
image of a luminous line, avc must study the march of the 
function u~^s>\\vxi. The roots occur when ri is any muhiplo 
of IT, except zero. The maximum vahic of tlio function is 
unity, and occurs when /< = (). Other maxima of rapidly dimi- 
nishing magnitude occur in positions not far removed from 
those lying midway between the roots. The image thus con- 
sists of a central band of half width corresponding to u = tt, 
accomjianied by lateral bands of Avidth tt, and of rapidly dimi- 
nishing brightness. The accompanying Table and diagram 
(Plato VII. fig. 1) will give a sufficient idea of the distribution 
of brightness for our purpose. 

Table I. 


?<-2siu- u. 

i u. 

u--&\i\- u. 






1 |t 












1 hi 







\ ^77 




^ 37r 


The curve A B C D represents the Aalues of u~'^ sin'- n from 
?/, = to ?< = 37r. The part corresponding to negative values 
of u is similar, A being a line of symmetry. 

Let us now consider the distribution of brightness in the 
image of a double line Avhose components are of equal sti-ength 
and at such an angular interval that the central \\\w in the 
image of one coincides with the first zero of brightness in the 
image of the other. Li fig. l-fhe curve of brightness for one 
coniponent is ABCD, and for the other OA'C; and the 
curve representing half the combined brightnesses is E' B E F. 
The brightness (corresponding to B) midway between the two 
central ])oints A, A' is -8100 of the brightness at the central 
points themselves. We may consider this to be about the 
limit of closeness at which there could be any decided appear- 
ance of resolution. Tlie obliquity corresponding to u — ir is 
such that the phases of the secondary waves range over a com- 
plete period, i. e. such that the projection of the horizontal 
aperture upon this direction is one wave-length. We conclude 
that a double, line cannot he fairhj resolved unless its compo- 
nents subtend an anr/le exceeding that subtended hy the irave- 
length of light at a distance equal to the horizontal aperture*, 

* lu the spoctrosco]ie tlie anpulnr witltli of the slit should not oxceeJ a 
moderate fraction of the angle dclincd in the text, if full resolving-power 
bo wanted. 

Lord Riiyleigh's Investigations in Optics. 


This rule is convenient on account of its simplicity ; and it 
is sufficiently accurate in view of the necessary uncertainty as 
to what exactly is meant by resolution. Perhaps in practice 
somewhat more favourable conditions are necessary to secure 
a resolution that would be thought satisfactory. 

If the angular interval between the components of the 
double line be half as great again as that supposed above, the 
brightness in the middle is -1802 (2 x •0901) as against 1-0450 
(l + "0450) at the central line. Such a falling off in the 
middle must be more than sufficient for resolution. If the 
angle subtended by the components of the double line be twice 
that subtended b}' the wave-length at a distance equal to the 
horizontal aperture, the central bands are just clear of one 
another, and there is a line of absolute blackness in the middle 
of the combined images. 

On the supposition that a certain horizontal aperture is 
available, a question (similar to that considered in § 1) arises, 
as to whether the whole of it ouo-ht to be used in order to ob- 
tain the highest possible resolviug-power. From fig, 1 we see 
that our object must be to depress the curve A B C D at the 
point B. Kow the phase of the resultant is that of the waves 
coming from the centre ; and at the obliquity corresponding 
to B the phases of the secondary wa^es range over half a 
period. It is not difficult to see that the removal of some of 
the central waves will depress the intensity-curve at B, not 
only absolutely, but relatively to the depression produced at 
A. In order to illustrate this question, I have calculated the 
illumination in the various directions on the supposition that 
one sixth of the horizontal aperture is blocked off' by a central 
screen. In this case the amplitude is represented by the func- 
tion/, where / ^^\ 

f=ii~^ (sinw— sin^j, . . . . (4) 

and, as usual, the intensity is represented by/^. 

Table II. 








+ -a333 


! l'^ 
















+ •1377 









+ •0043 











11 ,r 









Lord R;iyloigli\s Investigations in Oj>tics. 

The tliird uiid sixth columns show the inteiLsity in various 
directions rehitively to the intensity in the principal direction 
(« = 0); and the curve ABCD (fipr. 2) exhibits the same 
results to the eye. A comparison -with Tal)lc I. shows that a 
considerable advantage has been gained, the relative illumina- 
tion at B being reduced from '4053 to -3205. On the other 
hand, the augmented brightness of the first lateral band 
(towards C) may be unfavourable to good definition. The 
second bright lateral baud (towards D) is nearly obliterated. 
The curve E' B E V represents the resultant illumination due 
to a double line whose components are of the same strength, 
and at the same angular interval as before. The relatively 
much more decided drop at B indicates a considerable im- 
provement in resolving-power, at least on a double line of this 
degree of closeness. 

The increased importance of the first lateral band is a ne- 
cessary consequence of the stoppage of the central rays : for 
in this direction the resultant has a phase ojqwsite to that of 
the rays stopped. The defect may be avoided in great measure 
by blocking out rays somewhat removed from the centre on 
the tAvo sides, and allowing the central rays themselves to pass. 
As an example, I have taken the case in which the two parts 
stopped have each a width of one eighth of the whole aj)erture, 
with centres situated at the points of trisection (iig. 3). 

Fijr. 3. 


The function /' suitable to this case is readily proved to be 

/=?^~' (siuH— 2 sin - cos ^ J. . . . (5) 

The values of/ and /--^/ "2 are given in Table III.; and the 
intensity-curve ABCD is shown in fig. 4. 

Table III. 



r-^fo'- ' 




+ ■75 



— •2122 






- •01^.89 




■in 58 


+ •1125 



+ •1259 













•1043 1 

The depression at B is even greater than in fig. 2, while the 

Lord Rayleigh's Investigations in Optics. 269 

rise at C is much less. Probably this arrangement is about as 
efficient as any. 

I have endeavoured to test these conclusions experimentally 
with the spectroscope, using the double soda-line. The hori- 
zontal aperture of a single-prism instrument was narrowed by 
gradually advancing cardboard screens until there was scarcely 
any appearance of resolution. The interior rays were blocked 
out with vertical wires or needles, adjusted until they occupied 
the desired positions when seen through the telescope with 
eyepiece removed. With the arrangements either of fig. 2 or 
of fig. 4 a very decided improvement on the full aperture was 
observed ; but there was no distinct difference between these 
two arrangements themselves. Indeed, no such difference was 
to be expected, since the brightness of the first lateral band 
has no bad effect on the combined images, as appears from the 
curve E' B E F (fig. 2). Under other circumstances the in- 
fluence of the bright lateral band mioht be more unfavourable. 

In powerful spectroscopes the beam is often rendered un- 
symnictrical in brightness by absorption. In such cases an im- 
provement would probably be effected by stopping some of the 
rays on the preponderating side, for which purpose a sloping 
screen might be used giving a variable vertical aperture. It 
should be noticed, however, that it is only when the vertical 
apertui-e is constant that the image of a luminous line is im- 
mediately deducible from that of a luminous point. 

§ 3. Optical Po2cer of Spectroscopes. 

As the power of a telescope is measured by the closeness 
of the double stars which it can resolve, so the power of a 
spectroscope ought to be measured by the closeness of the 
closest double lines in the spectrum which it is competent to 
resolve. In this sense it is possible for one instrument to be 
more powerful than a second in one part of the spectrum, 
while in another part of the spectrum the second instrument 
is more powerful than the first. The most striking cases of 
this inversion occur M'hen one instrument is a diffraction-spec- 
troscope and the other a dispersion-spectroscope. If the in- 
struments are of equal power in the yellow region of the 
spectrum, the former will be the more powerful in the red, and 
the latter will be the more powerful in the green. In the 
present section I suppose the material and the workmanship 
to be perfect, and omit from consideration the effects of un- 
symmetrical absorption. Loss of light by reflection or by 
uniform absorption has no effect on resohing-power. After- 
wards I propose to examine the effect of some of the errors 
most likely to occur in practice. 

So far as relates to the dift'raction-gpecti-oscope, the problem 

270 Lord lliiyleigli's lacestvjat'wns in L>ptics. 

of the present section was solved in the PliiiosopLical Maga- 
zine for March 1874. I tluM-e sliowcd tluit if n denote the 
nmnher of lines on a grating and )n the order of the spectrum 
ohserved, a double lino of wave-lengths X, anil \ + hX will bo 
just resolved (according to the standard of resolution defined 
in the previous section), provided 

which shows that the resolving-power varies directly as m and 
n. When the ruling is very close, m is always small (not 
exceeding 3 or 4) ; and even when a considerable nund)er of 
spectra are formed, the use of an order higher than the third 
or fourth is often inconvenient in consequence of the over- 
lapping. But if the difHculty of ruling a grating may be 
measured by the total number of lines (n), it would seem 
that the intervals ought not to be so small as to preclude the 
convenient use of at least the' third and fourth spectra. 

In the case of the soda- double line the difference of wave- 
lengths is a very little more than yf/jo ; so that, according to 
(1), about 1000 lines are necessary for resolution in the first 
spectrum. By experiment I found 1130*. 

" Since a grating resolves in proportion to the total number 
of its grooves, it might be supposed that the defining-jjower 
depends on difierent principles in the case of gratings and 
prisms ; but the distinction is not fundamental. The limit to 
definition arises in both cases from the impossibility of repre- 
senting a line of light otherwise than by a band of finite though 
narrow width, the width in both cases depending on the hori- 
zontal aperture (for a given X). If a grating and a prism 
have the same horizontal aperture and dispersion, they will 
have equal resolving-powers on the spectrum." 

At the time the above paragraph was written, I was under 
the impression that the dispersion in a jn-ismatic instrument 
depended on so many variable elements that no simple theory 
of its resolving-power was to be expected. Last autumn, 
while engaged upon some experiments with prisms, I was 
much struck with the inferiority of their spectra in comparison 
with those which I was in the habit of obtaining from gratings, 
and was led to calculate the resolving-power. I then found that 
the theory of the resolving-power of prisms is almost as simple 
as that of gratings. 

* In my former jiapcr this number is -^qvcu as 1200. On reference to 
my notebook, 1 lind that I then took the full width of the gratinjr as an 
English inch. The .'5000 lines cover a Paris inch, whence the a]>ove cor- 
rection. From the nature of the case, however, the experiment docs not 
admit of much accm-acv. 

Lord Eayleigh's Investigations in Ojytics. 271 

Let Aq Bq (fig. 5) be a plane wave-surface of the light before 
it falls upon the prisms, A B the corresponding wave-surface 

Fig. 5. 

for a particular part of the spectrum after the light has passed 
the prism or after it has passed the eyepiece of the observino-- 
telescope. The path of a ray from the Avave-surface Ao Bq to 
A or B is determined by the condition that the optical distance, 
represented by \ fx, ds, is a minimum ; and as A B is by suppo- 
sition a wave-surface, this optical distance is the same for both 
points. Thus 

jVfZs(forA)=jVd.5(for B) (2) 

"SVe have now to consider the behaviour of lisrht belonaiuor 
to a neighbourmg part ot the spectrum. The path of a ray 
from the wave-surface Ay Bq to A is changed ; but in virtue 
of the minimum property the change may be neglected in cal- • 
culating the optical distance, as it influences the result by 
quantities of the second order only in the change of refrano-i- 
bility. Accordingly the optical distance from Ao Bq to A is 
represented by \{iu, + Sfi)ds, the integration being along the 
path Ao . . . A; and, similarly, the optical distance between A^Bq 
and B is represented by \ (fi + Sfx,)ds, where the integration is 
along the path Bo ... B. Li virtue of (2) the difference of the 
optical distances is 

JS/i ds (along Bo . . . B) — j S/^ ds (along Ao . . . A). . (3) 

The new wave-surface is formed in such a position that the 
optical ; distance is constant, and therefore the dispersion, or 
the angle through which the wave-surfiice is turned by the 
change in refrangibiiity, is found simply by dividing (3) by 
the distance A B. If, as in common flint-glass spectroscopes, 
there is only one dispersing substance, \ SfM ds = 8/j, . s, where ^ 
is simply the thickness traversed by the ray. If we call the 
width of the emergent beam a, the dispersion is represented 

by S/j, - — —, si and .\. being the thicknesses traversed by the 

extreme rays. In a properly constructed instrument i?i is. 

272 Lord Rjiyleii^h's Investigations in Oj>tics. 

negligible, and .<to is the aggregate thickness of the prisms at 
their thick ends, which we will call f ; so that the dispersion 
(6) is given by 

6='-^ (4) 

a ^ 

By § 2 the condition of resolution of a double line whose com- 
ponents subtend an angle 6 is that must exceed X.-=-a. Hence 
from (t), in order that a double lino may be resolved whose 
components have indices fi and /x + S/jl, it is necessary that t 
should exceed the ^alue given by the following equation, 

'=a7' ('> 

which expresses that the relative retardation of the extreme 
rays due to the change of refrangibihty is the same (\) as 
that incurred without a change of refrangibility when Ave pass 
from the principal direction to that corresponding to the first 
minimum of illumination. 

That the resolving-power of a prismatic spectroscope of 
given dispersive material is proportional to the total thickness 
used, without regard to the number, angles, or setting of the 
prisms, is a most important, perhaps the most important, pro- 
position in connexion with this subject. Hitherto in descrip- 
tions of spectroscopes for too much stress has been laid upon 
the amount of dispersion produced by the prisms ; but this 
element by itself tells nothing as to the power of an instru- 
ment. It is well known that by a sufficiently close approach 
to a grazing emergence the dispersion of a prism of given 
thickness may be increased without limit ; but there is no cor- 
responding gain in resolving-power. So for as resolving- 
power is concerned, it is a matter of indifference whether 
dispersion be effected by the prisms or by the telescope. Two 
things only are necessary: — first, to use a thickness exceeding 
that prescribed by (5) ; secondly, to narrow the beam until it 
can be received by the pupil of the eye, or rather, since with 
full aperture the eye is not a perfect instrument, until its width 
is not more than one-third or one-fourth of the diameter of 
the pupil. 

The value of expression (3) on which resolving-power de- 
pends is readily calculable in all cases of practical interest. 
For a compound prism of flint and crown, Bf/,.t is replaced by 

Sfi.t-SfM'.t', (H) 

Lord Eiiyleigh's Investigations in Optics. 273 

where t and t' denote the respective thicknesses traversed^ and 
hfi, Sfjb' the corresponding variations of refractive index. 

The relation between 8/j, and S\ may generally be obtained 
with sufficient approximation from Cauchy's formula 

/i = A + B\-2 (7) 


Sfx,= -2BX-^SX (8) 

The value of B varies of course according to the material of 
the prisms. As an example I will take Chance's ''extra-dense 
flint." The indices for C and the more refrangible T> are* 

so that 

/iiD= 1-650388, /xc = l-6U86Q; 

fMu-iMc = '00yo22 (9) 

Xd = 5-889x10"^ Xc = 6-5(32x10-', 

the unit of length being the centimetre ; whence by (7), 

B = -984xl0-'" (10) 

Thus bv (5) and (8), 

,= ^1_=J^^ (11) 

For the soda-line, 

\=5-889xlO"', S\ = -00(>xUr'; 

and thus the thickness necessary to resolve this line is given by 

^ = 1*02 centimetres (12) 

The number of times the power of a spectroscope exceeds that 
necessary to resolve the soda-lines might conveniently be taken 
as its practical measure. AVe learn from (12) that, according 
to this definition, the power of an instrument with simple 
prisms of "'' extra-dense glass" is expressed approximately by 
the number of centimetres of available thickness. 

In order to confirm this theory, I have made some observa- 
tions on the thickness necessary to resolve the soda-lines. 
The prism was of extra-dense glass of refractive index very 
nearly agreeing with that above specified, and had a refracting 
angle of 60°. Along one face sliding screens of cardboard 
were adapted, by which the horizontal aperture could be ad- 
justed until, in the judgment of the observer, the line was 

* Hopkuison, Proc. Roy. Soc. June 1877. 

271: Lord Riiyleigirs Iiiv€»ti<jationi< in Optics. 

barely resolved. A soda-flame was generally used, tlion<:;li 
similar observations have been made upon the D line ot" tiie 
solar spectrum. When the adjnstment was c'omj)lete, the apcr- 
• tnre along the face of the prism was measured, and gave at 
once the equivalent thickness, i. e. the diference ot" thicknesses 
traversed by the extreme rays, since the prism was in the posi- 
tion of minimum deviation. Care, of course, was taken that 
no ordinary optical imperfections of the apparatus interfered 
with the experiment. 

One observer, familiar with astronomical work, fixed the 
point of resolution when the thickness amounted to from 1"U0 
to 1*20 centimetre. I was myself less easily satisfied, requi- 
ring from 1*35 to 1'40 centimetre. But even with a less 
thickness than 1 centimetre, it was evident that the object 
under examination was not a single line. AV^ith the same 
prism I found the thickness necessary to resolve h^ h^ in the 
solar spectrum to be about 2*5 centimetres. According to (11), 
the thickness required for h^hi should be 2*2 times that 
required for D^ D2- Probably something depends upon the 
I'clative intensities of the component lines. 

From (1) and (11) we see that if a diflfraction and a dis- 
persion instrument have equal resolving-powers, 

■ t='^; (13) 

SO that the power of a dispersion instrument relatively to that 
of a diftVaction instrument varies inversely as the third power 
of the wave-length. 

For the kind of glass considered in (10), and for the region 
of the D lines, 

'=1-03^1006 (1"^ 

To find what thickness is necessary to rival the fourth spec- 
trum of a grating of 3000 lines, we have merely to put ??i = 4, 
71 = 3000; so that the necessary thickness is about 12i centi- 
metres — a result Avhich abundantly explains the observations 
which led me to calculate the power of prisms. 

Tcrling Place, 
August 12, 1879. 

[To be continued.] 


[ 275 ] 

XXXII. Measnrivq Polariscopes. 
By Professor W. Grylls Adams, M.A., F.U.S* 
[Plate yill.] 

SOME four years ago the description of a new measuring 
polariscope was communicated bj the author to the Phy- 
sical Society (see ' Proceedings,' voh i. p. 152), in which the 
advantages gained are an extensive field of view combined Avith 
accurate means of measuring the rings and the separation of 
the optic axes in biaxal crystals. The peculiarity of the in- 
strument consists in the arrangement of the two central lenses, 
one on each side of the crystal. These two lenses are plano- 
convex, very nearly hemispheres, and, with their flat surfaces 
inwards, form the two sides of a box to hold the crystal im- 
mersed in oil or a liquid ; they are so placed that their convex 
surfaces form portions of the same spherical surface. The 
crystal is placed in the box at the centre of curvature of the 
spherical surfaces of the two lenses. 

Two instruments have since been made on this principle 
with certain important modifications. In one, made by Mr. 
Tisley for horizontal projection (Plate VIII. fig. 1), the pola- 
rizer is a Nicol's prism capable of giving a clear parallel 
beam of polarized light 2^ inches in diameter: the middle 
portion of the instrument {i. e. the box with the two equal 
central lenses for its two opposite sides) has an opening at the 
top, into which the crystal to be measured is inserted, and is 
adjusted to its right position by a cup-and-socket motion. 
When the angle between the optic axes is to be measured, the 
instrument is placed with its axis horizontal, the crystal is 
placed with the plane of the optic axis vertical, the box and 
crystal together are then turned about a horizontal axis at 
right angles to the direction of the axis of the instrument, i. e. 
at right angles to the plane of the optic axes : thus either of 
the optic axes of the crystal may be made to coincide with 
the centre of the field of view, where the spider-lines cross one 
another, the angle through which the box is turned being 
measured to minutes by means of a circle attached to it and 
a vernier attached to the fixed stand supporting the instru- 

A table-polariscope on the same principle has been made by 
Herr Schneider of Vienna, into which several important mo- 
difications have been introduced. A section and view of the 
instrument are shown in figs. 2 and 3. 

The light falls on a plane mirror A, and is reflected into the 

* Communicated by the Physical Society, having been read at the 
Meetino: on June 28. 

27<) Prof. W. G. Adams on Measuring Polariscopes. 

instrument (whicli is placed with its axis vertical) through the 
first lens B, which is fixed on the tube in which the polarizer 
C is placed. 

D, E, F, G, and H (fig. 2) are lenses through which the light 
passes ; and K is a Nicol's prism (the analyzer). This part of 
the instrument foi'ms a complete table-polariscope of consider- 
able range. The Nicol's prism C and the lenses are supported 
each by means of two screws (shown in fig. 3), which may be 
moved upwards or downwards in two slots, and the lenses fixed 
in their proper positions- Between the plano-convex lenses E 
and F are the two central lenses L, M, two portions of a sphere, 
between which the crystal to be measured is })laced. The crystal 
should be immersed in oil. The setting of the lens L has a screw 
on its surface which fits into a screw in the setting of the other 
lens M, the arm supporting the lenses being a flat piece of 
metal one sixth of an inch thick, which is placed between them 
before they are screwed together. This arm, I, is supported 
by a stout crosspiece T, in the form of the arc of a circle which 
has its centre at the centre of curvature of the two lenses: the 
arc subtends nearly a right angle at the centre. It passes 
through and is supported by two guides P, Q, and has on its 
outer surface a rack which works with a small toothed wheel 
turned by the milled head N. 

On the upper face of the arm I is a train of toothed wheels, 
the setting of the lens M being provided with teeth, so that, by 
means of the milled head S on the outer wheel, the lenses and 
crystal may be turned about the axis of the instrument. 

The guides P and Q are attached to the face of a vertical 
circle which may be fastened by screws to a circular graduated 
rim R ; this rim is supported on and turns upon another fixed 
vertical circle, which is provided with verniers, so that the 
angle through which the rotating circle is turned can be mea- 
sured to one minute. The fixed circle is fastened to and car- 
ried by the piece of tubing holding the two lenses E and F, 
which is supported between the two pieces of tubing carrying 
the u})per and lower lenses. 

In this instrument the crystal can be turned about each of 
three axes which are mutually at right angles to one another. 

I. By turning the vertical circle and tubing to which it is 
attached, the crystal is turned about the vertical axis of the 

II. By turning the train of wheelwork the crystal can also 
be turned about an axis passing centrically through the cen- 
tral lenses, and the plane of its optic axes may be brought into 
the desired position for measurement. 

III. By turning the arc T by means of the milled head 

Phil. Mag. S. 5. Vol. 9. PiyiII.<\ 

Phil Mag R 5 Vol a P1V1I1.<; 

Systematic Classification of the various Forms of Energy. 277 

N, the axis of the central lenses may be made to coincide 
with the axis of the instrument ; the plane of the optic axes 
is then parallel to the vertical fixed circle, the crystal being 
turned by this motion about an axis bisecting the obtuse angle 
between the optic axes. 

IV. By turning the graduated circle ^^^th the arc T and the 
arm I attached to it on the face of the fixed vertical circle (/. e. 
round a horizontal axis perpendicular to the plane of the optic 
axes), and reading the verniers on both sides of the circle, the 
angles between the directions of the optic axes may be accu- 
rately measured. 

XXXIII. An Attempt at a Systematic Classification of the 
various Forms of Energy. 

To the Editors of the Philosophical Magazine and Journal. 


WHILE writing a little elementary manual of mechanics 
lately for Messrs. Chambers, my attention was di- 
rected to a certain amount of vagueness and loose langunge 
which appears to be current in modern statements concerning 

I venture, therefore, to ask you to publish in your Journal 
the following remarks on the subject, the greater part of which 
aim at embodying in a concise form what I understand to be 
the doctrines of the mathematical physicists (though they do 
not seem as yet to have been all clearly apprehended by phy- 
sicists in general), while the remaining portion contains a few 
points of view which have not, as far as I am aware, been 
published ; and though doubtless they have occurred to others 
besides myself, it would seem to be conducive to clearness of 
thought and accuracy of expression to have them briefly set 
forth in order, so that those which are erroneous or vague can 
be the better detected, and those which are true and definite 
can be the better apprehended. There can, I think, be little 
doubt that it may ultimately be possible, and that it is exceed- 
ingly desirable, to have all the fundamental doctrines of phy- 
sics stated in ordinary language without technicalities ; but 
unless such statements are accurate and devoid of vagueness, 
they can be of little or no use. 

It will, I hope, be understood that tlic following attempts 
at statements are in a dogmatic form simjjly in order to be con- 
cise. Some improvement in the present language of text- 
books is distinctly desirable ; and I hope that this communi- 
cation may be sufficiently suggestive to lead to a discussion, 

Phil. Mag. S. 5. Vol. 8. No. 49. Oct. 1870. U 

278 Dr. 0. J. Lodge on a St/steniatic Clasmijicatioii 

or to an autlioritutivo stattMiicnt which shall conduce to abetter 
understanding of the matter than is at present general. 
1 am, Gentlemen, 

Your obedient Servant, 

Olivku J. Lodge. 

1. Every action which takes place between two bodies* is 
of the nature of a strcf^s. A stress consists of two equal op- 
posite forces (called action and reaction, or force and anti- 
force), one of them exerted by the one body, and the other by 
the other ; and it is impossible for one force to be exerted 
without the other. 

2. Whenever a body exerting a force moves in the sense 
of the force it exerts, it is said to do ztwA-f; and whenever a 
body exerting a force moves in the sense opposite to that of 
the force it exerts, it is said to have work done upon it, or to 
do anti-work, the quantity of the work being measured in each 
case by the product of the force into the distance moved 
through in its own direction. 

3. Whenever two bodies exert a stress on each other, they 
are in contact ; and if they move, they inove together over 
the same distance |: hence, since the force equals the anti- 
force, the work done by the one in any movement is equal to 
the anti-work done by the other. 

4. The working-power§ of a body is measured by the average 
force it can exert, multiplied by the range or distance through 
which it can exert it. The working-power of a body may be 
increased or diminished by increasing or diminishing either 
the force, or its range, or both ; and it must remain dormant 
so long as external circumstances do not allow it to exert a 
force through a distance. 

5. Whenever work is done upon a body, an efl'ect is pro- 
duced in it which is found to increase the working-power of 

* The terra bvily is here used in its most general sense, viz. as standing 
for a piece of matter in general, without regard to size. It may mean a 
planet or an atom ; and it may even apply to such extra-material things 
as the {Bthcr and the Jiypothetical ultra-mimdano corpuscles, or to any 
tiling else which is suiliciently like ordinary matter to be capable of pos- 
sessing energy and of doing work therewith. 

t It Seem* preferable to speak of the work as being done by the hodij 
rather than by tlie force ; though the latter expression is unduubtedly 
convenient sometimes. 

X This step is rendered necessary by the preceding one of considering 
the work as done by the body. If it is the torco which does the work, it 
is unnecessary. 

§ Or power of doing work. But either term is objectionable, because 
poicer means rate of doi'iif/ work. The term entropy has been used, but I 
believe that the accepted connotation of this vrovd is now diHerent. 

of the various Forms of Energy. 279 

that body (bv an amount not greater than the work done); 
hence this etiect is called energy, and it is measured by the 
quantity of work done in producing it *. Whenever work is 
done hy a body, i. e. anti-work done on it, its working-power 
is found to be diminished (to at least the extent of the work 
done), and it is said to have lost energy — the energy lost 
being measured, as before, by the anti-work done in destroy- 
ing it. 

6. But in every action taking place between two bodies the 
work is equal to the antiwork ( § 3) ; hence the energy gained 
by the first body is equal to the energy lost by the second ; or, 
on the whole, energy is neither produced nor destroyed, but 
is simply transferred from the second body to the first. (Re- 
member footnote to § 1.) 

To summarize then : — Work creates energy ; anti-work 
destroys it ; so both together simply transfer it. Or, in other 
words, the transference of energy requu'es a stress to act 
through a distance, and involves therefore two equal opposite 
works. If it were possible to obtain a force without its anti- 
force, or if it were possible for two bodies exerting stress on 
one another to move over unequal distances (§ 3), then it would 
be possible to obtain work without the anti-work, and thus to 
get a source of new energy (technically called the Perpetual 
Motion); but, as a fact of experience, it is not possible. 

7. "When work is done upon a body, different kinds of 
effects can be produced, depending both on the nature of the 
body and on the way in which the forces doing the work are 

* This definition of energy, as the effect produced in a body by an act of 
work, is not so simple as the usual one — '•' the power of doing work ;"' but 
this latter definition seems a little unhappy. For energy is power of doing 
work in precisely the aame sense as capital is the power of buying goods. 
Now a sovereign has an infinite power of buying goods if it has any at all 
— twenty-shillings worth being bought whenever it is transferred from 
one man to another. The proper statement is that a sovereign usually 
confers upon the man that possesses it a certain buying-power, which power 
he loses when he has transferred it ; and in this sense money is a power 
of buying goods. It does not, however, necessarily confer upon its owner 
any buying-power,- because there may not be any accessible person to buy 
from ; and if there be, he may have nothing to sell. Just so with energy : 
it usually, though not necesarily (see § 14), confei*s upon the body pos- 
sessing it acertain power of doing work, which power it loses when it has 
transferred it. The analogy here indicated will be found useful in teaching. 

Energy corresponds to capital. 

Doing work corresponds to buying. 

Doing antiwork corresponds to selling. 

The transfer of capital is accompanied by two equal opposite acts, buy- 
ing and selling ; and it is impossible for one to go on without the other. 
Hence the algebraic sum of all the buying in the world is always zero : this 
is the law of the conservation of capital. 


280 Dr. 0. J. LoJ^o on a Si/ste>natic Classi/ication 

applied to it ; and tliese constitute the ditlerent forms of 

8. We can proceed to classify the forms of energy by first 
of all considering how the effects produced depend upon the 
forces applied to the body. 

If these forces have no resultant (/. c. if they are in equili- 
brium), the body will he alraineif, and will exert a correspond- 
ing stress. 

If the forces have a result;int, the body will l)e moved*; 
and the motion will be either a translation or a rotation, or 
both, according as the forces can be reduced to a single finite 
resultant, a resultant zero at infinity, or to both combined. 

Similarly, the strain may be analyzed into compression, elonga- 
tion, and shear, or a eombhiatiou of them, according to the way 
the forces act ; but this division does not appear to be of much use 
for our present purpose. 

All these effects arc forms of energy, because the working- 
power of the body in which they are produced is in general 
increased; i. e. the body is rendered capable of doing work as 
soon as the proper condition is supplied. (See § 4.) 

Thus a steadily strained elastic body is exerting force or 
pressure; but its point of application is stationary: allow it to 
move, and work is immediately done. A body in free motion 
is passing through space, but it is not exerting any force ; 
supply a resistance, and work is immediately done. 

5^'. Energy, therefore, has two principal forms : — 

(1) The free motion of bodies relatively to one another; 

(2) The separation of bodies from one another against stress. 
And to these may be added for convenience the rapid alter- 
nation from one form to the other, called vibration. 

10. The two fundamental forms of energy correspond to 
the two factors in the product workf. A body exerting force 
possesses energy, and a body moving through space possesses 
energy ; but a body is not doing work unless it is hath exert- 
ing force and moving through space. 

* And possibly strained as well. It is only forces wliich like gravity 
act uniformly on every particle of a body that can move an ordinary elastic 
solid without straining it. 

t Energy and work are not to be confounded together ; and all such 
phrases as "accumidated work,'' " conservation of work," "conversion of 
heat into work," " work consumed," &c., shoidd be eschewed. Energy 
is not work, biit work can be got out of it if the proper condition be sup- 
plied. It is in fact possibh' work. 

The expression j)ossei/e cwryt/, however, is meaningless; so also is the 
expression actual energy. All energy is actual and real — pc^tential just as 
much as kinetic; and all represents possible icurk — that is, work that 
will become actual as soon as the other factor is supplied. 

of the various Forms of Energy. 281 

The energy possessed by matter in motion is called Kinetic. 
The enerory possessed by matter exerting force is called Poten- 
tial. It might -with great propriety be called Di/namic energy; 
and it has been very conveniently called Static energy*, in op- 
position to kinetic. Of the t^Yo factors F and s, then, in the 
product work, kinetic energy corresponds to s; there is motion 
through space, but no force : potential energy corresponds to 
F ; there is force, but no motion. 

11. "Whenever work is being done, both factors must be 
present — that is, both kinetic and potential energy ; and the 
energy is always passing from one of these forms into the 
other while the work is being done. For if the motion of a 
body is tcith the force which acts upon it, its speed must in- 
crease ; and if the motion is against the force, the speed nmst 
decrease; while in the first case the available distance through 
which the force can act, or the range of the force, is decreasing, 
in the second increasing. 

12. The groups into which the forms of energy have been 
arranged (§ 8) — viz. strain, rotation, translation, and vibra- 
tion — may now be subdivided further, by considering how the 
effects produced when work is done upon a body depend 
upon its nature and size. 

A convenient division of bodies, according to size, will be — 
1st. Masses comparable in size with the human body: 

which may be called ordinarj' masses. 
2nd. Masses incomparably larger, as planets. 
3rd. Masses incom[)arably smaller, as particles or mole- 
4th. The ultimate atoms. 
All these material bodies agree in general properties, and 
differ only in size. But distinct apparently from these there 
exists an unknown something, which is material enough to be 
capable of possessing energy, to disturbances in which electrical 
phenomena seem to be due, and of which probably an aspect 
has been called a5ther. This must therefore constitute a 5th 
group, differing from the others apparently in respect of na- 
ture, not of size. 

13. All these groups of bodies may be strained or set in 
motion in various ways when work is done upon them ; and 
the groups into which the known forms of energy are thus 
thrown are exhibited provisionally in the following Table. 

* The cause of the stress exerted by a strained body in any particular 
case is not in general kno-svn, and it may easily turn out often to be ulti- 
mately due to a kinetic phenomenon, as it certainly is in the case of the 
sti'ess exerted by a compressed gas ; nevertheless it may still be called 
static energy so long as the cause of the stress is not mider consideration. 

2&2 Dr. 0. J. Lodge on a Systematic Classification 







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. 1 










































of the various Forms of Energij. 283 

[The numbers in the compartments are merely for convenience 
of reference.] 

It is quite possible that the form of energy indicated in compart- 
ment No. 4 would be better placed in Xo. 8, those now in No. 8 
being placed in Xo. 12 ; but I have placed them as they now stand 
because they are closely connected with the vibration-forms in the 
same rows. Moreover the true position of gravitation energy cannot 
be properly defined till we know more about it. It may have to 
come under the kinetic head — the motion of Le Sage's corpuscles. 

Probably the arrangement of the forms in the last row may be 
improved, but I am not sufficiently acquainted with the Maxwellian 
theory to do it, Neither do I know whether one is justified in 
pointing out an analogy between the two forms of strain indicated 
in No. 20 and simple and torsional shear, — or whether one may 
imagine that the volume-elasticity and Young's modulus of the 
"something" are infinite, but that its rigidity is finite though high. 
An apparently consistent though rather hazy mental image of some 
obscure phenomena may be built up on a basis like this ; but it is 
too speculative to be mentioned further here. 

14. The power of doing work conferred upon a body by the 
possession of energy does not depend upon the absolute quan- 
tity of that energy only, but on its transferability. If it is 
not transferable, the body possessing it has no power of doing 

15. Energy Avhich can be guided, and all, or nearly all, 
transferred to any body at pleasure, is called a high or avail- 
able form of energy, and is said to be capable of doing " useful " 
work, this woi'k being done every time it is transferred in 
desired directions. 

Energy which is nearly incapable of being guided, and 
which transfers itself in directions not required, is called a Ioav 
or unavailable form of energy ; and the work done at each of 
its undesired transfers is called " useless " work*. 

16. The distinction between high and low forms of energy 
is a relative one, and depends on our present power of dealing 
with matter. 

Masses of matter comparable to our own bodies in size can 
be handled and dealt -with singly ; and so they can in general 
be caused to do work upon, and therefore transfer their energy 
at pleasure to, any of the numerous accessible bodies which 

* The distinction between useful and useless work is quite accidental, 
and belongs more to economics tlian to physics. An engineer will often de- 
gi-ade the whole of a large quantity of energy in order to produce some 
superficial result wliicli he happens to desire at the moment, e. //. when a 
planing-macliine smooths a surface ; or when a locomotive transfers pas- 
sengers or goods between places on the same level. 

284 Dr. 0. J. TakIi^c on a Si/.'^leuialir Classification 

are competent to receive it. Hence energy possessed by them 
is generally of a bigli form. 

17. Planetary masses can be dealt Avitb singly indeed, but 
so singly that there is scarcely* any other body accessible to 
Avhich their motion can be transferredf (see §§4 and 14). 

18. The energy of moving molecules is not very available 
to us, because we can only deal with them statistically and 
not individually. There is a hirge amount of relative motion 
and transference of energy constantly going on among indi- 
vidual molecules ; but, as we have no control over it, the work 
done is useless, and the energy imavailable. The only ]iart of 
the energy which can be transferred at will to external bodies 
is that due to the average state of the moving molecules ; and 
it is not possible to transfer even this unless some other mass 
is accessible, the average state of wliose molecules in respect of 
motion or strain is in some way different, so that the one is 
able to do work upon the other J. 

Xow since all accessible bodies have very large stores of 
molecular energy, it follows that a very great portion of the 
energy which belongs to the molecules of a body must be 
totally unavailable to us, because it can never be got rid of or 
transferred. And even the portion Avhich can be transferred 
at pleasure to some larger body, if not made use of quickly, 
will be found to transfer itself to nei";hbourini; molecules and 
in directions not required, and will waste itself in doing use- 
less work. Hence molecular energy is called a low form. 

19. Atomic or chemical energy seems at present to rank 
a httle higher than molecular energy ; for though one way of 
availing ourselves of it is by converting it into molecular 
energy (heat) and then doing useful work with the balance of 
the averaiie effect bv which the body heated excels its neijih- 
hours, yet animals and galvanic batteries are able to do useful 
work with it in a more direct and less wasteful fashion. 

* The well-known exception is the ocean, which by the agency of the 
moon is put into a slightly difterent state of motion from the rest of the 
eartli ; and a minute portion of the earth's cncrg}- of rotation is constantly 
being transferred to it. A portion of this tidal energy is now available to 
us, and may be made to do useful work. 

t Hence the kinetic energy of the earth is of no more use to us than a 
bank-note to Ilobinson Crusoe. 

I An analogy may be drawn between the molecular energy of a body 
and the money of a bank ; of which a reserve fund is kept for internal 
transfer and transactions between customers, while the excess gets invested 
in external concerns which have a deficiency, and so becomes available 
for doing useful work. To make the analogy more complete, the clerks 
should be uniformly dishonest, or the coffers insecure, so that stored 
money should dribble away. 

of the various Forms of Energy. 285 

The unknown, or electrical, energy appears to rank distinctly 
above the energy of molecules ; because we have found some 
remarkable and indirect means of transferring the energy of 
electric currents to ordinary masses, by the intervention of 
electromagnetism, with a comparatively small waste. 

20. When energy passes from a higher to a lower form it 
is said to be degraded ; and when it has no availability at all 
it is called dissipated*. 

Energy is degraded when it is transferred from masses of 
ordinary size to the molecules of which they or others consist 

(§ 18). 

The two fundamental forms of energy are those due to mo- 
tion and those due to strain (§ 9). Now Avhenever motion 
takes place against friction, some energy is always transferred 
to the molecules of the rubbing surfaces. And whenever strain 
is produced in imperfectly elastic bodies, some energy always 
passes to the molecules. 

But in practice no motion takes place without friction, and 
all bodies are imperfectly elastic. Hence energy is continually 
getting dissipated ; or, in other words, at every transfer of 
energy between ordinary bodies under ordinary circumstances, 
some of it is always and necessarily degraded into a lower and 
less available formt. 

It may be useful to append the following summary of the 
contents of the sections : — 

1. Newton's third law. 

2. Definition of work, + and — . 

3. Denial of "action at a distance." 

4. Definition of working-power. 

5. Definition of energy. 

6. Conservation of energy, and first law of thermodynamics. 

7. Possibility of various forms of energy. 

8. Classification of the forms of energy." 

9. The fundamental forms of energy. 

10. Kinetic and potential energy are related to the two fac- 
tors in the product work. 

• It is then of no more use to us than is our money to the inhabitants of 
Mars, who ha^e no means of getting at it. Its terrestrial transferences 
are to tliem useless. 

_ t For instance, during every quarter-swing of a free pendulum, energy 
IS bemg transformed from kinetic to potential, or vice versa ; and is heing 
transferred from the unknown gravitation agent to the mass of the pen" 
didum, or back again. Some, however, is dissipated every time, and ulti- 
mately the pendulum must stop. 

28(> 31 r. AN'. Baily on a Mode of 

11. Transformation Ironi one ionn to the other. 

12. Furtlior subdivision ol" t]\c ibnns of cnoro y, 

13. Classitication tablo. 

14. Distinction between energy and \YLat was once called 


15. Distinction between available and unavailable energy; 

and between nseful and nseless work. 
l(j. Reason why the energy of ordinary masses is available. 

17. Reason why ])lanetary energy is almost nnavailable. 

18. Reasons why molecular oiergy is much of it unavailable ; 

and second law of thermodynamics. 
10. Extent of availability of atomic and of electrical energy. 
20. Dissipation of energy. 

XXXIV. A Mode of prodncinft Arago's Rotation. 

Bij Walter Baily, M.A* 

[Plates IX. & X.] 

ARAGO'S method of producing rotation in a copper disk 
consists of suspending it by its centre so as to make it 
lie horizontally above the poles of a horseshoe magnet, and 
then rotating the magnet about a vertical axis. The rotation 
of the disk is due to that of the magnetic field in which it is 
suspended; and we should expect that if a similar motion of 
the field could be produced by any other means, the result 
would be a similar motion of the disk. 

Possibly the rotation of the magnet ma}' be the only prac- 
ticable way of producing a uniform rotation of the tield ; but 
it will be shown in this paper that the disk can be made to 
rotate by an intermittent rotation of the field etfected by means 
of electromagnets. 

Sup})ose two magnetic poles to be below a plane sheet of a 
conducting substance ca})able of moving in its own plane. 
Each pole may be regarded as a small circular current parallel 
to the disk. The currents will be in the same or different di- 
rections according as the poles are of the same or ditt'erent 
names. We will examine the effect of a change in the strength 
of either of the poles, in giving the sheet a tendency to move. 

There are four cases ; viz. — 

1. Poles alike. One increasing. 

2. „ „ One diminishing. 

3. Poles unlike. One increasing. 

4. „ „ One diminishing. 

* Communicated by the Physical Society, having been read at the 
Meeting on June 28. 

Phil. MaP.S. 5.V0I. 9.P1.1X. 


Fig. 1. 

B'. A'. 

Fig. 2. 



Fig. 4. 



Fi2. 3. 

Mintem Bros lilh. 

Phil. Mag. S. B.Vol.S.Pl.X. 

rig. 5. 





Fig. 6. 


Mntem Bros lith. 

producing Arago's Rotation. 287 

In case (1) the increasing pole induces in the portion of the 
sheet opposite to itself a circulai c"rrent opposite in direction 
to the currents representing the poles. Hence this portion of 
the sheet is repelled by both poles. The repulsion from the 
increasing pole is perpendicular to the sheet, and gives it no 
tendency to moye ; but the repulsion from the other pole tends 
to move the sheet from the constant pole toward the one which 
is increasing. 

In case (2) the diminishing pole induces in the portion of 
the sheet opposite to it a circular current in the same direction 
as those representing the poles ; so that this portion of the 
disk is attracted by both poles, and the disk tends to move from 
the diminishing pole toward the one which is constant. 

In cases (3) and (4) it can easily be shown that the results 
are the opposite to those obtained in cases (1) and (2) respec- 

If one pole increases while the other diminishes, both ten- 
dencies to move are in the same direction, and the resulting 
tendency is the sum of the two. 

The pole of an electromagnet made or broken is the extreme 
case of a pole increasing or diminishing. 

Now conceive an even number of vertical bar electromao- 
nets arranged in a circle with their upper poles in one hori- 
zontal plane, and a copper disk to be suspended above them ; 
and the two magnets at the extremities of each diameter to be 
coupled together, and with a battery, so that each such pair 
of magnets forms a horseshoe electromagnet independent of 
all the others. Let P, Q, R, S be pairs of magnets at the 
ends of successive diameters. Make P, and then make Q so 
that the north pole of Q is adjacent to the north pole of P, 
and therefore the south pole of Q adjacent to the south pole 
of P. Then by case (1) the portion of the disk opposite the 
north pole of P is driven towards the north pole of Q ; and a 
similar action takes place at the south poles. Now break P. 
By case (2) the portion opposite the north pole of P is again 
driven towards the north pole of Q, and so with the south 
poles. Continuing the action by making R and then break- 
ing Q, making S and then breaking R, and so on, in each 
case making the adjacent poles similar, we g(^i a series of im- 
pulses on the disk all tending to make it move in one direc- 
tion round the axis of suspension. Hence the disk will rotate 
as in Arago's experiment. 

In one extreme case, viz. when the number of electromag- 
nets is infinite, we have the case of a uniform rotation of the 
magnetic field, such as we obtain by rotating permanent 














7. 8. 








288 Mr. W. Baily on a Mode of 

In the other extreme case the number of pairs of electro- 
manrnets is reduced to two, and the number of batteries is also 
reduced to two. Let the poles of one })air of magnets be called 
a, a', and those of the other b, U. Then the arrangement of the 

pole as seen from above is i/ /; and the successive states of 

these poles will bo 




N, S, representing north and south poles respectively, and 
representing that the pole is not magnetic. It appears that 
the change from 1 to 3 through 2 is nothing more than rever- 
sing a a' ; and the change from 3 to 5 consists in reversing 
b b'. Similarly we pass from 5 to 7 by reversing a a' , and 
again from 7 to 1 by reversing bb'. The whole process is 
thus shown to consist in reversing a a' and b // alternately. 

In passing from 8 to 1 Ave see by case (1) that the parts of 
the disk over b, b' are respectively repelled from «, o! \ and by 
case (3) we see that the same parts are respectively attracted 
to a', a. Again in passing from 1 to 2 we see by case (2) 
that the parts above a, o! are respectively attracted by Z», //; 
and Ave also see by case (4) that the same parts are respec- 
tively repelled by // b. 

The effect of each of these tAA'o changes is to make the disk 
tend to rotate in the direction aba' b'. All the other chan rjes 
may be shoAA-n to have the same effect ; so that the disk Avill 
rotate in the direction a b a' b'. 

If starting Avith the state (1) avc rcA'crse bb' tirst, Ave should 
have the series of states as follows : — 

1. 2. 3. 4. r,. G. 7. 8. 1. 

from Avhich it may be easily shoAvn that the disk Avould rotate 
in the direction b a b' a'. 

The experiment Avith the four electromagnets may be readily 
performed by means of a connnutator Avhich will reverse the 
currents several times in a second ; and a considerable rotation 
can be given to the disk. 

The commutator Avhich I constructed for the experiment 
consisted of a Avheel of wood with a brass rim. This rim Avas 
completely cut through in places equidistant from each other ; 
and ten tongues of thin co})per pressed against the rim*. 

* The number of cut? must not be less than seven. I used eight cuts. 

producing Arago's Rotation. 289 

These tongues were in two groups of five ; and in each group 
the distances between the contacts of the tongues with the rim 
were half the distances between the cuts in the rim. The dis- 
tance between the two groups must be greater than the dis- 
tance between the contacts. 

Let A be a wire from the positive pole of our battery, 
and A^ A'^ be wires from the negative pole of the same battery; 
B a wire from the positive pole of the other battery, and B' B" 
wires from the negative pole ; and let a a' be the ends of the 
coil round one pair of electromagnets, and h V the ends of the 
coil round the other pair. In the figures 1 to 4 the wheel is 
seen in four consecutive positions, with the tongues in contact 
with it ; and the letters show with what wire each tongue is 

The contact of two tongues with the same section of the 
ring puts the wires to them into electric connexion. 

The connexions are, in 




A' a'. 





A a', 






A a', 






A a, 

A.' a', 





A a, 

A.' a', 



Hence in passing from fig. 1 to fig. 2 the current through 
a a' is reversed ; in passing to fig. 3 that through h h' is re- 
versed. The current through a a' is reversed again in passing 
to fig. 4, and that through h V is reversed again in passing to 
fig. 1. The commutator is thus seen to reverse each pair of 
magnets twice while rotating through the angle subtended by 
one division of the rim ; so that with eight divisions one turn 
of the wheel reverses each pair of magnets sixteen times. 

If the wheel is rotated in the opposite direction, the series 
of magnetic states is obtained in the reverse order, and the disk 
rotates in the opposite direction. But there is a better me- 
thod of reversing the motion of the disk — which is, to introduce 
an ordinary commutator into one of the circuits, either between 
the battery and the wheel, or between the wheel and the mag- 
nets. The reversal of this commutator reverses the motion, 
while the wheel is rotated continuously in one direction. 
Fig. 5 gives the arrangement of the connexions. A, B are 
the batteries ; a, a', &, h' the electromagnets ; C the ordinary 
commutator ; and D the wheel. 

It should be noted that the rotation of the disk is accom- 
panied by the formation of induced currents whose intensity 
depends on the velocity of rotation, and whose effect is to di- 
minish the rotation. These opposing currents are got rid of 

200 Mr. 11. K. M. BosaiKiuct on the Pre.^enl 

Avlion tlio disk is snspeiulod as a torsion-balanco, and its defloc- 
tion observed, as the currents Avill not be I'urnied except wlieu 
the tlisk is movino-. 

The eftbet on the disk niitrht bo niucli increased by placinfij 
four other electromagnets above the disk, each opposite one of 
tlio lo\A'er niaoncts, as connected with it, so that the lower pole 
of the upper magnet should be of the opposite name to the 
uj)per pole of the lower magnet. In fig. G one pair of mag- 
nets is shown with the opposite pair, and the wires connecting 
them. The disk is seen in section, balanced on a needle-point, 
between the two pairs of magnets. The other four magnets 
are not shown in the figure. 

XXXV. On the Presient State of Experimental Acoustics, with 
Suggestions for the Arrangement of an Acoustic Lahorator if, 
and a Sketch of Research. Bg K. H. M. Bosanquet, St. 
Johns College, Camhridge. 

To the Editors of the Philosophical Magazine and Journal. 


THE following paper presents an outline of suggested ar- 
rangements and work for an acoustic laboratory, which 
I hope shortly to be able to carry out. I have thought that 
it may be of interest to the readers of the Philosophical 
Magazine. Yours truly, 

R. H. M. Bosanquet. 

Experimental acoustics are at present in a condition which 
is perhaps not entirely satisfactory. In the teaching of the 
subject there is occasionally more demand upon the faith of 
the learner than is altogether desirable in an experimental 
science. I think that tliis arises from the difficulty of access 
to those experiments which deal witli the foundations of the 
science. The prices charged for complete sets of acoustic ap- 
paratus are enough to show that the possession of such appa- 
ratus must Ije confined to few. Adequate sets of such apparatus, 
used in a sufiicient and convincing manner, are exceedingly 
rare. Under these circumstances, that full experimental 
knowledge which is desirable in a science of this description 
does not generally exist. 

The ordinary apparatus and arrangements for demonstration 
appear to err in some points. The efiects are not produced in 
a continuous manner, but by fits and starts, generally by 
bowing on the sounding body. We do not analyze with ease 

State of Experimental Acoustics. 291 

and certainty a phenomenon which only presents itself to dis- 
appear again. These intermittent phenomena are generally 
produced by an eftbrt, often requiring considerable skill. 
Under these circumstances there is a tendency to accept the 
first conclusion that comes to hand, the mind being to some 
extent satisfied with the production of the difficult pheno- 
menon. Again it has become perhaps too much the practice 
to refer the phenomena to optical analysis or analogy. In 
some cases this reference is, no doubt, most convenient ; in 
other cases it is misleading. It is requisite that the analysis 
of the perceptions of the ear be conducted by reference to the 
ear itself. 

The only form of apparatus in use for the production of 
simple tones in a continuous manner depends on the applica- 
tion to resonators of tuning-forks driven by electromagnets. 
These are in many respects ill adapted for demonstration, 
though no doubt thev have furnished most valuable results. 
There appears to be a want of adaptability about the apparatus; 
and it is very costly. Professor Konig is probably better ac- 
quainted with the practical use of this apparatus than any one 
else, except perhaps Helmholtz himself; and Konig has, in an 
elaborate analysis of the phenomena *, controverted the entire 
foundations of the work of Helmholtz. Opinions are by no 
means at one on the subject, even amongst the highest autho- 

With the object of improving the treatment of this part of 
the subject, I have introduced resonators which speak in the 
manner of organ-pipes. These resonators are easily managed 
with a little simple organ-mechanism ; they receive their wind 
through flexible tubes, and can be placed in any part of the 
room, at any distance apart, kc. — a matter of great importance 
in facilitating the analysis of the phenomena. The resonators 
are fitted with siphons and reservoirs ; by a simple contrivance 
of this kind thev can be tuned to anv note within range at a 
moment s notice. 

These resonators are made out of bottles, corks, and metal 
organ-pipes. Their cost is trifling. 

The notes should be perfectly pure tones, according to the 
theory, having regard only to disturbances of the smallest 
order: but practically, in all tones of this supposed pure cha- 
racter small quantities of harmonics do exist ; and I have long 
maintained that they always must exist in sensible intensity, 
on account of the transforming power of the air, or, in other 

* Pog^. Ann. clvii. p. 177 ; Phil. Mag. [V.] i. pp. 417, 511. See also 
' Proceedings of Musical Association,' 1878-70. Spottiswoode " On Beats 
and Combination-tones."' 

2!»2 Mr. R. 11. M. Bosanquot on the Present 

words, because the aerial disturbances of highor orders are 
never small enougli to be entirely neglected*. The lower har- 
monics can be accordingly detected in the notes of these 
resonators by the use of analyzing resonators of proper pitch, 
whose interiors communicate with the ear. The twelfth can 
be detected by an experienced ear, in some cases, without the 
use of analyzing resonators. 

Section of speaking resonator, with organ-pipe mouthpieco, siphon with 
atop, and reservoir for tuning; also flexible tube for putting into the 
ear when used as an analyzing resonator. This tube can be also used lor 
gas-flame experiments. 

With a rough experimental bellows furnishing an unsteady 
wind, and these resonators, I have been able to repeat some of 
the less difficult of the experiments of Konig. 

The only statement made by Konig as to the notes of which 
the beats consist, is in Phil. Mag. fifth series, i. p. 425, where 
he says that the two notes of a harmonic interval appear alter- 
nately, but that the observation is difficult in the case of the 
octave. Now in all cases where beats exist, it is possible, by 
the use of analyzing resonators communicating with the ear, 
to determine in the manner pointed out by Helmholtz the dif- 
ferent notes which vary in intensity, as well as any that do 
not vary in intensity. But Konig does not appear to have 
attempted this analysis at all. 

In the cases I have examined I have succeeded in determi- 
ning the notes which were beating. In this determination, 
which is sometimes of difficulty, I found it useful not only to 
employ the analyzing resonators, but to move them about, as 

* See abstract of a paper " On the Condition? of the Transformation of 
Pendulum- Vibrations,'^ Koport of British Association, 1870 (Transactions 
of Sections, p. 4->). 

State of Experimental Acoustics. 293 

well as the primary notes, until the effects were most distinctly 
obtained. Stationary nodes and loops are formed in the room 
for all the notes present; and by taking advantage of these the 
analysis may be much assisted. 

Curious results are undoubtedly obtained. For instance, the 
beats of an octave slightly out of tune are almost entirely on 
the lower note. If the notes are kept apart in the room, the 
upper one appears quite steady ; while the lower one varies 
much in intensity, whether we listen to it with the unassisted 
ear or with a resonator. With the assistance of a resonator 
the much smaller variation of the upper note can be detected. 
These two phenomena are not separated by Konig, but de- 
scribed simply as a beat. According to Helmholtz, the beat of 
the lower note would be due to the ditference-tone, thatof the 
upper note to the octave harmonic of the lower note interfering 
Avith the upper one. Now it is easy to convince oneself with 
the analyzing resonator that the latter interpretation of the 
beat of the upper note is right : one can hear separately the 
octave harmonic and the octave note, as well as the beat itself. 
But the explanation of the beat of the lower note, as due to 
the interference of the difference-tone, presents this difficulty. 
If we run up the lower note by means of the siphon, the dif- 
ference-tone should become audible. But Avith the arrange- 
ments I employed no trace of difference-tone could be per- 
ceived, even when the octave was run up to a fifth and a sen- 
sitive resonator employed to detect the difference-tone. The 
notes were placed far apart ; and the arrangement was, no 
doubt, not favourable to the production of a difference-tone : 
but then how could it be there, so as to form these strong beats 
of the lower note, if it was not loud enough to be heard sepa- 
rately ? I have only stated the above with the object of show- 
ing that there is a large ground here, important in a theore- 
tical point of view, which will repay careful working. In fact 
the repetition and examination of the large collections of ex- 
periments in the work of Konig above cited, with the notes of 
such resonators as I have described, or with pure notes equally 
powerful and manageable, is a work essential to the establish- 
ment of the foundations of the theory of the subject. 

I have come to the conclusion that it is not practicable to 
carry the work much further with this apparatus without a 
much steadier wind. For this purpose it is desirable to con- 
struct improved bellows. No existing pattern (except that of 
Cavaille Coll) delivers a wind of any thing like the steadiness 
desirable. I shall return to this question later. 

Although with an improved bellows hand blowing would 
be admissible, yet it is always difficult to secure uniformity in 

Phil Mag. S. 5. Vol. 8. No. 49. Oct. 1879. X 

294 Mr. 11. H. M. Bosanquot on the Present 

hand-l)lown wind ; and -whore those investigations arc to bo 
made on any hu'<re scale it will be preferable to employ a small 
engine, of a kind aftbrding uniibrm rates of motion, for this 
as well as for many other acoustic experiments. 

This suggestion forms the key to a conce})tion of an acoustic 
laboratory, which is, I believe, new, and would, it seems to 
me, constitute a considerable step from an ex{)erimental point 
of view. This is, that, in an acoustic laboratory, })ower should 
be employed to produce all the ett'ects required, in a continuous 
manner where continuity is suitable, and without eil^brt or 
attention on the part of the investigator when the experiment 
is once arranged. It is easily seen that determinations of all 
sorts, which now present almost insuperable difficulties, would 
become perfectly easy under such conditions : and accurate 
knowledge A\'ould soon take the place of many of our guesses 
of today, through numberless extensions of the work now pos- 

I proceed to mention the principal other 'subjects which 
suggest themselves as suitable for research under these con- 

Aerial Mechanics generally. 

So far as our knowledge of the mechanics of fluids, and 
especially of the air, has progressed beyond its elements of late 
years, the progress has been mainly in the mathematics of the 
subject. No doubt the deficiency of experiments arises mainly 
from the difficult nature of the subject matter; but it is also 
certainly due to the small extent to which real eflbrt has been 
made to devise experiments of easy and certain execution, which 
shall supplement and check the mathematical investigations. 
No doubt a beginning has been made, and the exjieriments 
which are known have been made to tell their tale with admi- 
rable perseverance and ingenuity ; but it is my opinion that 
the mathematical structure has, in some respects, been built 
up too rapidly. 

The questions which arise are of great difficulty ; and I do 
not purpose here to enter on any of them. It is sufficient to 
say that I believe there will be no difficulty in devising a 
number of experiments by which the simpler cases of aerial 
motion may be examined in detail. Until the whole circum- 
stances of crucial experiments of this kind have been made cut 
experimentally, I shall continue to feel grave doubts as to the 
stability of certain portions of the mathematical edifice. 

I may allude to a lew experiments of importance. Much 
has been built on a mathematical solution of the tbllowing 
problem: — If a circular disk, closing a circular hole in an in- 
finite plane, execute oscillations at right angles to the plane, 

State of Experimental Acoustics. 295 

what is the motion thereby imparted to the surrounding air ? 
There is a question how far the sohitious of this problem, 
which have been given, conform to the fiicts. The experi- 
mental settlement of this question is quite possible ; and it 
goes to the yery foundation of a certain portion of the mathe- 
matical equations upon which the modem theory is built. 

Again, the equivalence of sound with mechanical energy is 
at present in the position of a mathematical speculation. Tlw 
establishment of this equivalence, with a systematic mode of 
measurement, and the determination of the various laws on 
which it depends, is a work which alone would constitute an 
important research. I shall return to this later. 

There is another important question in aerial mechanics, 
which calls for mention among the very first. The whole 
theory as now developed, neglects intentionally the viscosity 
of the air. ]S"ow the effects of viscosity are more easily dealt 
■sA-ith by experiment than by theory. It is pretty certain that 
the effects of viscosity are not really negligible ; for if they 
were, vortex rings could not be produced in air, nor could 
they be extinguished when once produced ; and in fact, as we 
all know, they can be produced, and are rapidly extinguished. 
The actualcompositionofthe notes produced by the various 
methods which aim at the production of simple tones is also 
a matter of primary importance, which no attempt is being 
made to settle. It is certain that the existing explanation of 
even such a simple matter as the overtones of organ-pipes is 
insufficient ; for speaking resonators, whose overtones should 
by theory be inharmonious, give true harmonics, of small in- 
tensity, indeed, but with a general effect not very dissimilar to 
that heretofore supposed to be peculiar to stopped organ-pipes. 
It is possible that the organ-pipe mouth is responsible for 
much more than has been supposed. 

I have noticed these points only as specimens of aerial me- 
chanics. The oscillating disk first mentioned will be easily 
constructed, and serve for numerous experiments of this class. 
On the whole, ex^^erimental aerial mechanics must be regarded 
as, in the future, probably the most important part of experi- 
mental acoustics. 

Vibration Kumhers. 

The accurate determination of the vibration numbers or fre- 
quencies of notes is at present a matter of great difficulty. 
AYhere many such determinations are to be made, the employ- 
ment of a small engine possessing a uniform rate of speed, 
conti'olled by a contrivance to be described later, will place 
this part of the subject on a new footing. The siren, the re- 
volving stopcock (described later and already constructed), 


£96 I\rr. 1\. H. M. Bosanquet on the Present 

tlio old toothcd-wliool a])para(iis, and tlic flasliin^r maeliine of 
Lord KayK'igli arc examples orinstruincnts wliieh will acquire 
a new importiince for this purpose when driven by a uniform 

Revolving Stopcock. 

There is a large class of investigations which depend on the 
regular opening and closing of a channel, for the interruption 
either of a current of wind or of a current of sound. A turn- 
table fitted with revolving sto|)cocks has been constructed for 
these investigations; and rough results are obtained without 
difficulty ; but it is only by the einjiloyment of the uniform 
motor that accurate results can be expected. 

The dissi])ation of sound in resonators and organ-pipes is a 
problem which may be attacked by means of the interrupted 
current of wind. What is the length of a periodic interrup- 
tion in the wind-supply of a pipe or resonator which just fails 
to break the continuity of the tone? The answer to this ques- 
tion, and the phenomena we come across in the process of ob- 
taining it, furnish important contributions towards our know- 
ledge of aerial mechanics. 

Another problem depending on interrupted wind-supply is, 
the determination of the velocity of sound in the open air for 
different musical notes, by a process bearing some slight ana- 
logy to Fizeau's detennination of the velocity of light by re- 
flection from a distance. The corridor of a cloister supplies 
an excellent locale. The sound is emitted by the apparatus at 
such intervals that a number of echoes (4, 6, or 8) are heard 
between two suct3essivc sounds. The mode of calculation is 

A problem depending on the interrupted current of sound 
is, If the ear listen to a sound through the interrupted channel, 
what are the phenomena ])resented ? They are of some com- 
plexity and considerable interest. Professor Mayer has pub- 
lished experiments on the subject. 


Notwithstanding the investigations that exist on the beha- 
viour of reeds with respect to columns of air with which they 
are connected, the subject is still involved in considerable ob- 
scurity. There arc different kinds of reeds, which possess very 
different properties ; and there is ample room for a thorough 
experimental investigation. With the appliances of the pro- 
posed laboratory these investigations are within reach. 

The revolving stopcock can be used to admit wind to the 
bottom of a pipe or resonator, and so separate out those effects 
which mav be regarded as the results of inexorable motions of 

State of Experimental Acoustics. 297 

reeds from those in which the reeds are influenced by the re- 
action of the resonator. This arrangement gives rise to a 
beautiful set of experiments having many bearings. The 
trouble of maintaining the constant motion of the turn-table 
is very great ; and it is practically impossible to obtain definite 
results without the uniform motor. 

This arrangement, where the stopcock delivers wind into a 
pipe or resonator having the same vibration-frequency as that 
of the jet of the stopcock, gives a smooth powerful tone : it is 
well fitted for the evaluation of a sound of given loudness in 
terms of mechanical energy. I shall return to this point. 


The conditions of the flow of sound-energy from strings, 
through sound-boards, into the surrounding air require inves- 
tigation. The case of practical interest is that of the \aolin. 
By arranging a sort of skeleton so as to represent the principal 
parts of the instrument, and employing mechanical bowing, 
it is expected that some light may be thrown on this obscure 
subject. This question is as yet untouched ; but it is probable 
that the bridge and sound-post transmit a longitudinal vibra- 
tion, which is communicated to the back at the point Avhere it 
meets the sound-post at right angles. The effect of " muting," 
or loading the bridge with a small weight, comes in as a ques- 
tion for explanation. 

Orchestral Instruments. 

The study of the theory of orchestral instruments is in its 
infancy. Tlie theory of the fingering of the wood wind — flute, 
hautboy (oboe), clarionet, bassoon — appears likely to be for the 
most part tolerably straight forward. The cases where two or 
more segments of a tube affect each other, though there are 
open holes between, form a problem which is untouched. 

The law that in all lip reed-instruments the note produced 
is a resonance-note of the tube, was enunciated and proved 
first by Mr. Blaikley (see ' Proceedings of the Musical Asso- 
ciation,' 1877-78, p. 56). On the same occasion I stated that 
I had obtained and proved the same law experimentally for 
the hautboy and clarionet (l. c. p. 62). TV e may therefore take 
as the basis of our work the proposition that, when reeds of 
movable pitch form notes in combination with a variable reso- 
nance, the note produced coincides with a note of resonance. 
This is not true for reeds of fixed pitch associated with a reso- 
nance, as in organ reed-|)ipes, according to the best practical 

The study of the partial tones of columns of air, such as are 

208 IMr. R. H. M. Bosauquet on the Present 

enclosed in ordinary brass instruments, is of high practical 
iniportiinco. This study has lately for the first time been 
put on a sound footing by Mr. Blaikley (/. c). The exami- 
nation of diti'erent forms opens up a considerable field of work. 

Changes of Temperature. 

The effect of changes of temperature on sounding columns 
of air, tuning-forks, and other sounding bodies, still requires 
investigation. It remains unexplained, for instance, why 
small organ-pipes are more affected by changes of temperature 
than lar^e ones. The accurate laws of the change remain also 
to be ascertained. 

Velocity of Sound in Tubes. 

The laws of the variation of the velocity of musical sounds 
of different pitch, in tubes of varying diameter, have been for- 
mulated*; but the results obtained by different investigators 
do not agree, and this important element is consequently un- 
certain to quite a considerable extent. There appears to be 
no reason why this should not be cleared up by the use of 
proper appliances. 

Quality of Organ-pipes. 

The mechanical conditions under which sound of different 
qualities is produced are not uuderstood in all cases. We 
know empirically that an organ-pipe of large diameter gives 
a pure tone. In fact the largest-scaled open organ-pipes have 
their fundamentals so predominant that analysis by beats fails 
to detect any harmonics. For investigations as to the lowest 
limit of audible sounds there is, therefore, no apparatus to be 
compared with a large-scale 32-foot open diapason as it stands 
on the organ. The notion that stopped pipes are preferable is a 
mistake. Whether it be that stopped pipes are not made of suf- 
ficiently large scale I do not know; but it is generally easy to 
demonstrate, by a simple process of analysis by beats, that 
stopped pipes drop their fundamental about the middle of the 
32-foot octave, or at about 25 vibrations per second, whereas 
with open 32's the fundamental remains approximately un- 
mixed to the very lowest pair of notes. As we diminish the 
depth of the pipe from back to front, the predominance of the 
fundamental diminishes ; and as we continue, we come to a 
point Avhere the pipe cannot be made to speak its fundamental 
at all. Further investigation is required. 

* See Pogg. Ann. rew series, ii. p. 235; also Pogg. Ann. cxxxiv. 
\\ 177. 

State of Experimental Acoustics. 299 

Sympathy and Draiving. 
Under certain circnmstances two sources of sound react on 
each other, and affect either the pitch or intensity with which 
they would speak separately. When two organ-pipes of the 
same pitch weaken each other's intensity, there is said to be 
" sympathy." When two of different pitch affect the pitch in 
which they mutually speak, there is said to be " drawing." 
Lord Rayleigh brought forward some cases of the latter (see 
Proc. Musical Assoc. 1878-79, p. 20), in which the pipes 
spoke the same note, lying above the pitch of either separately: 
this was with open pipes. I have observed a case where two 
stopped pipes " drew " together to a note below the pitch of 
either separately. This mutual influence also occurs with har- 
monium-reeds. With organ-pipes it presents an interesting 
problem of atmospheric vibrations. With harmonium-reeds it 
is practically important in connexion with the construction of 
tonometers. This subject remains almost unworked. 

Loudness of Sound. Mechanical Eqrdvcdent of Sound. 

The subject of the measurement of the loudness of sound 
will receive a new foundation in the admission of Fechner's 
psycho-physical law, with respect to the perception of sound 
by the ear*. This law is derived from the admission that 
equal fractions of any existing mechanical intensity produce 
equal unpressions ; and it results in the statement that the im- 
pression is the logarithm of the mechanical intensity. 

Under these circumstances impressions have to be classified 
as to apparent loudness, in the same manner as stars are clas- 
sified as to apparent brightness. The criterion of successive 
stages is that they appear equally distinct from one another 
when loudness onlv is considered. The followine; is a sketch 
of such a classification. 

Audible sounds are divided into ten magnitudes. The first 
magnitude includes the loudest sounds. The magnitudes down 
to the fifth include lesser sounds that are still loud ; the sixth 
to the tenth magnitude includes sounds that are not loud, the 
tenth magnitude containing the softest sounds that can bo 
heard. The distinction between loud and not loud is very- 
definite to my ear ; it may not be equally so to others. Of 
course the following list represents only my own impressions, 
and it may probably require amendment when considered by 
others. Each magnitude includes the sounds up to the next 
on the loud side. 

* See Helmlioltz, Phys. Optik, p. 312. * Xineteeutli Century,' July 
1879, p. 166, Galton (where the law is called Weber's law). 


300 Mr. I^. IT. M. Bosnnquct C7t tic rrcacnt 

Tlic organ is mucli used in the dcscriiition, as by reference to 
it magnitudes can bo described in ii uay that is intelligible to 
a large number of persons. Stops of average voicing are to 
be understood, not in the swell-box unless stated. The sound 
is supposed to be heard in a church or hall of moderate size. 

The estimate is to l)e formed purely as to loudness; and for 
this purpose it is advisal^le to compare unmusical noises. 


f 1. Steam ■whit5tlt>. Cannon close Ly. Cburcli bells in the chamber. 

2. Troniba (tuba niirabilis). Sounds of (1) at a little distance. 
Loud bells at foot of tower. 

3. Full organ without tromba. 

4. Trumpet with diapasons. Siug-ing or public spealang at the top 
of the voice. 

5. Moderu loud diapasons (German). Loud singing or intoning. 
Ordinary public speaking. 

G. Soft diapasons (old English). Soft singing or intoning. Loudest 
ordinary conversation. 

7. 4 choir 8-foot stops. Ordinaiy speech. 

8. Stopped diapason alone. Soft speech. 

"o 9. Dulciana. Strong whisper. Tick uf watcli close to ear. 
^ I 10. Dulciana or salicioual (in swell-box closed). Faintest whisper. 
(. Tick of watch at arm's length. 

Great precision is not attempted ; but it is generally easy 
to say whereabouts in the scale a given sound lies. Precision 
will come in time. 

Several problems then lie before us: — 

(1) What is the common ratio of the mechanical intensity 
in two successive magnitudes ? 

(2) What is the absolute value of the mechanical intensity 
corresponding to one definite magnitude ? 

(3) What is the law of the dependence of the magnitude of 
sound of given mechanical intensity on variation of pitch. 

As to the first two I have made some rough determinations; 
but the apparatus at my disposal is too imperfect to enable 
me to quote the results as being of any value. With a better 
bellows I see no difiiculty in the way of answering these two 

* Since the above was written I have made a determination of the ratio 
by observations of" Tom," Christ Church, Oxford, when tlie 101 strokes 
are rung, after 9 p.m. At the foot of the tower, say 30 yards off the source, 
it was of 2nd magnitude; at the distance of If mile, of 10th magnitude. 
This gives for the common ratio of the mechanical energy for two conse- 
cutive magnitudes, 1 : 3-2 nearly. The experiment with a resonator above 
referred to, gave 1 : 2-3 for the common ratio, iVom an estimated difference 
of two magnitudes, the estimate being of course very uncertain. The 

State of Experimental Acoustics. 301 

As lo (3), I showed some years ago* that, on certain sup- 
positions which cannot be very far from the truth, the energy 
of notes of different pitch and the same loudness varies as the 
wave-leno-th. The other conclusions drawn at that time were 
based on the supposition that mechanical intensity was a true 
measure of the impression on the sense. The arrangements 
now described will furnish the means of examining this point 
in other ways. 

(4) When sounds of different pitch excite different parts of 
the sensorium, it appears probable that Fechner's law applies 
to each part separately. It is quite certain that a single soft 
stop sounding the octave below is detected at once, if added to 
the full organ without such stops ; whereas the addition of a 
similar stop, having the same pitch as any part of the sound 
actually present, could not be detected by the most experienced 
ear. This part of the investigation is as yet untouched. 

Phonograph and Plionautograph. 

These instruments consist of devices for producing marks 
characteristic of sounds on a moving surface, generally a cy- 
linder which rotates uniformly. The uniform motor will give 
to the results of these instruments a completeness which they 
now generally fail to possess. It has hitherto been almost 
impossible to obtain, for instance, phonographic records of 
musical sounds, on account of the uncertainty of the speed of 
rotation ; and the exact reproduction of such sounds from the 
phonograph has presented great difficulties, if, indeed, it has 
ever been accomplished. 

The most interesting applications of the phonograph, how- 
ever, are to the analysis of speech. Tlie forms corresponding 
to different vowels have been determined by Messrs. Jenkin 
and Ewing ('Nature,' xviii. pp. 167, 340, 394, 454). But 
the point in which the proposed arrangements will be of most 
value is in the analysis of the inflections of speech, or the rapid 
variations of pitch which occur continually. This analysis is 
of the highest importance for phonology, as the inflections are 
undoubtedly among the principal characteristics of dialects. 
The employment of the uniform motor in connexion with these 
recording instruments promises the easy solution of this 

observation of •' Tom "' is by no means final ; besides the disturbing influ- 
ence of buildings, &c., a ligbt breeze got up at the time of the distant ob- 
servation. But the determination seems worth quoting; indeed it can- 
not, I think, be verv far wTong. 
* Phil. Mag. 1872; xliv. p. 381. 

302 Mr. R. H. M. Bosiinquet on the Present 

Electro-j^ncximatic Clock Governor. 

In all tlio applications of power useful for acoustic purposes, 
every tliinf^ turns n})Oii the steadiness of the motor and its 
accurate n^^ulation. I propose to indicate in outline how the 
pneumatic and electro-pneumatic apparatus in use amon^ 
organ-builders will furnish convenient means of automatic 
regulation by the clock. 

A good clock will close an electric circuit at every beat of 
the pendulum for a time which must not be too short. This 
current will communicate with an ap])aratus such as is em- 
ployed in the electric action of the organ, in Avhich air is ad- 
mitted from a reservoir to a small power-bellows on closing 
the circuit. In this way a ratchet-wheel will be pushed for- 
ward a step every second. This drives a bevel wheel on the 
same axis. Another bevel wheel opposite, moving freely on 
the same axis, is turned in the opposite direction by the ma- 
chine to be regulated. A third bevel Avheel, with movable 
axis at right angles to the tirst axis, gears in the other two 
wheels. If the two other wheels move in op})osite directions 
with equal speed, the third simply turns round on its axis. If 
either of the tirst two goes quicker or slower than the other, 
the axis of the third moves with half the ditferential velocity. 
If this axis be attached to the governing arrangement of the 
motor, the whole number of revolutions of the machine per- 
formed in any length of time can be constrained to preserve 
any desired ratio to the movement derived from the clock. 

The details would occupy more space than is desirable. I 
will only say that pneumatic apparatus can be freely used with 
advantage. The ordinary pneumatic key, connected with its 
work by tiexible tubing, and touched by a stud on the spindle 
of any part of the machine to be controlled, forms a most 
valuable resource for automatic regulation. 

Pneumatic Motors. 
It will not be generally convenient to drive more than one 
machine at regulated speed from the same motor. For this 
and other reasons the employnient of secondary motors, driven 
from the bellows, will probably be of advantage. The form I 
propose to give to these instruments is that of a three-crank 
shaft and flywheel, with three power-bellows attached to the 
three cranks. They will also be controlled by the clock 
governor, with the assistance both of governed su})ply and 
pneumatic brake. For the finer regulation of speeds I anti 
cipate that the best results will be thus obtained. 

State of Expanmental Acoustics. 303 

Bellows of Precision. 

The only bellows of precision that I know of is that of 
Cavaille Coll*: it is expensive; the complete machine costs 
£80. I will state shortly the principles on which the obtain- 
ing of steady wind from the feed depends ; it will appear that 
it is not necessary to increase largely the cost of the ordinary 

The simplest form of supply is one feeder driven by the up- 
and-do\Nni motion of a handle, the stroke overcoming also the 
weio;ht of the feeder. This arrangement discharges a volume 
of air into the reservoir with a uniform velocity, which begins 
and ends suddenly : the weight of the feeder always caus(?s a 
shock at the beginning and end of the stroke. The area of the 
feeder is generally equal to the area of the reservoir, so that 
the velocity imparted by the stroke to the top board of the 
reservoir is half that of the lift of the end of the feeder. This 
is the worst form of supply ; it is common in very small organs. 

In all cases the reservoir must be made with one inverted 
and one direct rib. This is well understood by organ-builders. 

The next best form of feed is that common in English 
organs. Two equal feeders, each occupying half the area of 
the reservoir, are moved in opposite directions by up-and-down 
strokes of a handle. The feeders balance and the shock is ma- 
terially lessened. The velocity of the upper board is a quarter 
the lift of the end of the feeder. But the stroke is still generally 
made with uniform velocity, beginning and ending suddenly. 

The next improvement is the application of a pair of cranks, 
axle, and fly-wheel to the previous combination. In this case 
there are two discharges for each turn of the fly-wheel, whose 
velocities follow the pendulum-law. The velocity alternates 
between zero and its maximum. Great smoothness is here 
attainable so long as the speed is low; but at high speeds the 
variation of the velocity of supply will be objectionable. 

This inconvenience may be to a great extent obviated by 
using three feeders instead of two, the three feeders being 
worked by three cranks on a shaft, set at angles of 120°. The 
velocity of supply in this case has maxima and minima at in- 
tervals of 30° ; but these maxima and minima are in the ratio 
of 2 : •>/3, or 1 : 0"866 nearly. This variation is less than 
that obtained by using four feeders, but it is more frequent. 
The value, however, is so nearly unitbrm that it is not thought 
that any considerable gain would result by increasing the 
number. If more exact uniformity were desired, six feeders 
at intervals of 60° would give exceedingly small variations of 

* Comptes Rendus,l^Q^,\.^.^9, 'Nature," xviii. p. 381. 

304 On the Present State of Experimental Acoustics. 

the total velocity of supply, Avbich would be absolutely the 
same at points 30° apart. The wci<rhts of the feeders being 
borne by the cranks, it is of no consequence that they do not 
absolutely compensate each other. 

The escajie-valves open into the feeders in the best modern 
work ; the supply then ceases without noise or shock when the 
bellows is full. 

The principle here applied is that of making the feed of 
wind itself steady ; the plan more commonly adopted has been 
to employ appliances to overcome the effect of the unsteadi- 
ness of the suppl}-. 

The arrangement is, I believe, not new; but I do not know 
of any particular instance where it is in use. It is suitable for 
the employment of power. Governing arrangements can be 

It would be desirable that a lathe should form part of the 
laboratory fittings. With this assistance the more expensive 
and novel forms of apparatus might be constructed in the labo- 
ratory itself — such as new forms of the siren, oscillating disks, 
revolving stopcocks, clock governors, &c. 

The most suitable engine that I have seen for the purpose 
is Eider^s hot-air engine. This is worked by a certain definite 
mass of air alternating between a hot and cold cylinder, the 
two plungers working in cranks at right angles. It is the 
most silent engine that I have seen; and the smallest size of ^ 
H. P. can be Avorked with a gas-burner. Independently of 
its suitability for laboratory purposes, it is an extremely pretty 
bit of practical thermodynamics. 

So far as I am aware, no laboratory has been fitted with 
arrangements of the nature of those I have described. The 
plan seems to me worth trying; and I hope before long to 
make an effort to carry it out. 

The cost of the whole of the new apparatus is hardly likely 
to amount to that of a set of tuning-forks of Konig and a 
"■ soufflerie de precision " of Cavaille Coll together. It seems 
likely to do away with the need of a great part of the expen- 
sive apparatus formerly required for these purposes; but I do 
not suppose that it will be desirable to be altogether without 
the older apparatus. The experiments of Konig, for instance, 
can hardly be said to be repeated unless they are repeated to 
some extent under the original conditions; and the comparison 
of different methods may be expected to lead to instructive 
results. Electromagnetic forks are unquestional)ly of great 
importance, and for some purposes cannot be replaced, though 
for large departments of work we may with advantage find 
substitutes for them. 

On the Influence of Atomic Weight. 305 

If such a laboratory should be fitted up, it would probably 
be coutemplated that iustructiou should be given, ultimately 
at least, as well as research undertaken. But the locale Avhich 
would be sutHcient for research would not necessarily be suit- 
able for lecturing or other instruction. 

XXXVI. Influence of Atomic Weight. By Thomas Car- 
KELLEY, Jj.Sc, Assistmit Lecturer on Chemistry in the 
Owens College*. 

THE object of the present paper is to point out the influ- 
ence which the atomic weights of the elements have on 
the chemical, and especially the physical, properties of both 
elements and compounds. 

As early as 182(3, Gmelin (and subsequently Pettinkofer, 
Dumas, Kremers, Gladstone, Cooke, Low, Odling, Fleay, &c.) 
directed attention to some curious relations between the atomic 
weights of certain classes of elements and also between their 
properties. Many of such relations will at once suggest them- 
selves. Thus, of the elements CI, Br^^ and I, bromine stands 
almost midway between chlorine and iodine, both as regards 
its atomic weight and its chemical and physical properties. 


gravity of Melting-! Boiling- L^eat evolved 
the liquid . pointt? | pointt. V union wuh 
elements.;^ T j one atom H. 



Mean of CI and 1 = 


1-33 at 15=! 193 , 240 , 2.3783 
4-00 at 107°, 387 ' 473 j - S'JOG 
2-66 292 1 356 i 10(t^8 
2-99 at 15° 248 j 331 | 9322 

Very similar relations exist between Ca, Sr, and Ba, of 
which Sr holds a position almost intermediate between the 
other two ; but what has been said with regard to CI, Br, I, 
will be quite sufficient to illustrate the kind of relations which 
were pointed out at the time referred to. It was not, how- 
ever, till within the last fifteen years that these relations were 
first traced in a systematic manner ; and it is to Xewlands, 
and especially to Mendeljeff, that we owe a new field of research 
and a new and powerful method of attacking chemical prob- 
lems. The importance of the work of Xewlands and Mendel- 
jeff" cannot be easily overrated. The principle proposed inde- 
pendently by each of them will serve in the future, and has 
done to some extent already, to indicate those directions in 

* Commuiucated by the Author. 

t Reckoned from a'hsohite zero —273. 

30G Dr. T. I'anu'Uey on the 

wliicli rosonrcli is most needed Jind in ^vllit•ll fliero is most pvd- 
mi:;c ol' inleiestino- results. Tlic application of tins jjrineiplo 
■will also enable us to make predictions of })henoinena still lui- 
known, and will at the same time prevent many fruitless 
researches. It is and Avill be, in fact, for some time to come 
the finoer-post of chemical science. 

Notwithstanding the importance of this subject, it has up to 
the ]n'esent been very much neglected. For though Mendel- 
jeff's results are well known, yet the details and the service 
which his Periodic Law offers in the prosecution of chemical 
research are tar from being so. Were his memoir more ge- 
nerally read, and the methods he proposes more widely applied, 
many fruitless researches would be avoided, and many impor- 
tant problems would be solved far more readily than is gene- 
rally the case at present. 

Up to within the last few years the Avork of the chemist has 
been very largely to collect facts. Now, however, the great ten- 
dency is to generalize, connect together, and ofl^'er some expla- 
nation of these facts. Thus, take a given element. Why should 
it possess certain properties and another element certain other 
properties ? And what connexion is there between the ditferent 
jiroperties of the same element ? What, for instance, consti- 
tutes the trud diflterence between Ag and CI, and why are they 
different ? Why should silver melt only at 1000° C. and be a 
heavy solid at the ordinary tem})erature, whilst chlorine is a 
gas, very much less dense than silver? Why should silver 
have a great affinity for bromine, whilst chlorine has but very 
slight affinity for it? The greatest and highest object of the 
chemist and physicist, therefore, is to endeavour to offer some 
explanation of these and of a host of similar phenomena, and 
to get as near as possible at the root of the matter. In 18G4 
Newlands made the first great step in advance, which advance 
was increased and placed on a firmer basis by ]\lendeljeff in 

The stage at which we have now arrived, and at which work 
is still being carried on ■with ever increasing activity, is the 
tracing of the interconnexion of properties. For this purpose, 
what we have to do is to find what properties vary regularly 
with other properties. A well-known example of this is Du- 
long and Petit's law of " Specific Heats," according to which 
the specific heat of an element is inversely as its atomic weight; 
also Gay-Lussac's law of vapour-density, which states that 
the vapour-density of a gas = ^ its molecular weight. Also, 
I have recently shoAvn (Devt. chcm. Ges. Ber. xii. p. 440, 
March 1879) that the greater the coefficient of expansion of 
the elements by heat the lower the melting-point. And more 

Injiuence of Atomic Weight. 307 

recently M. Eaoul Pictet (Comjyt. Bend. Ixxxviii. p. 855, 
April 28, 187l») lias fixed this relation still more exactly; for 
he concludes: — (1) The liigher the melting-point of a solid, 
the shorter are the oscillations of its molecules. (2) The 
melting-points of solids correspond to equal lengths of oscilla- 
tion ; and therefore the product of the length of oscillation by 
the melting-point is constant for all solids. Or, expressed in 
the form of an equation. 

t X =c; 

where t = melting-point, reckoned from —273, a = coefiicient 
of expansion, d = specific gravity, p = atomic weight, and 
c = constant. 

If we can prove that one or more certain properties all varv 
regularly with a certain other property, and if "\ve can off'er 
some explanation of this last property, we are in a fair way of 
being able to explain the other properties. Thus it has already 
been pointed out that, the higher the melting-point of an 
element, the less is its coefficient of expansion ; and it can be 
easily shown that both theso phenomena are dependent on the 
attraction between the molecules. It is generally allowed that 
in the solid condition the forces which draw the molecules 
together are greater than those which tend to drive them 
apart. In the liquid condition the opposing forces are more 
equally balanced, and the molecules move freely over one an- 
other. In the state of gas, on the other hand, the i-epulsive 
force is stronger than the attracting, and the body tills the 
whole space in which it is placed. If, then, a substance melts 
when the repulsive force = attracting force (and the repulsive 
force, Ave know, is due to heat), then it follows that the greater 
the attraction between the molecules of a body the greater will 
be the heat required to melt it. Consequently, if we compare 
a number of bodies at the ordinary temperature, their melting- 
points will be the higher the greater the attraction between 
their molecules, because the greater the heat required to over- 
come that attraction. "We may therefore say that the melting- 
point of a body is proportional to the attraction between its 
molecules, when there is no repulsive force acting, i. e. at the 
absolute zero of temperature. If this be true, then we can 
easily see that the melting-point of a substance ought to bear 
some relation to its coefficient of expansion, hardness, <tc,, 
since these properties are evidently dependent on the attraction 
between their molecules ; for the greater the attraction between 
the molecules of a body, the greater will be the heat required 

308 Dr. T. Carnellcy on the 

to drive tho niolocules apart, and thorofore tho less will it ex- 
pand on bein^ heated ; and consequently the greater the coefti- 
cient of expansion the lower the melting-point. The two 
phenomena of fusion and expansion by heat thus admit of a 
common explanation, viz. the attraction between the molecules. 
Again, the greater the attraction between the molecules of a 
body the greater the e.vfernal force required to separate them 
mechanically, and therefore the harder the body. If this be 
true, then the hardness of a body ought to 1)ear some relation 
to its melting-point. We actually find that, as a general rule, 
the harder a body the higher its melting-point: thus diamond, 
steel, &c. have a" very high melting-point and great hardness, 
whilst lead, potassium, sodium, wax, &c., have a low melting- 
point and are soft. This relation, however, is not so regular 
and easily traced as in the case of the melting-point and co- 
efficient of expansion, the reason being that the separating 
force (viz. heat) in the case of fusion and expansion is exerted 
internally, and therefore more uniformly than in the Ciise of 
determining the hardness of a body, for in the latter the sepa- 
rating force is exerted externally* . 

Quincke (' Watts's Diet.' vii. p. 241) has shown that the 
order of capillarit}' of metals in the solid state is the same as 
their order of hardness ; and this is what we might expect. 
Bettone (Pogg. Ann. cl. p. 644) has determined the hardness 
of the elements by finding the time required for a steel drill 
to penetrate to a certain depth, and has by this means shown 

sp. fr. 1 

that the hardness of an element = ~~' . = r? ^^^ fol- 

at. wt. sp. vol. 

lowing being a few examples out of a large number given in the 

original memoir : — 

Ilarcluess. r 

spec. vol. 

Diamond .... 0-301 -202 

Iron 0-137 '137 

Copper .... 0-13l) '136 

Platinum .... 0-109 -111 

Zinc 0-108 -108 

Silver 0-099 -096 

Tin 0-005 -062 

Lead 0-057 -055 

Potassium . . . 0-023 "022 

* The first part of the present paper was wi-itteu in the summer of 1878, 
and read before the Owens-Collego Cheniical Society, January 1870, since 
when an article by F. Mohr, "On Cohesion,"' has appeared in Licbig's ^«- 
nak-n, cxcvi. p. 194 (1879), in -which he points out that the metals form a 
"scale of hardness agreeing closely with the order of their melting-points." 

Influence of Atomic Weight. 309 

Now it has already been pointed out that the harder a body 
the higher is its melting-point ; and as the hardness likewise 
varies inversely as the specific volume, therefore the greater 
the specific volume of an element the lower ought its melting- 
point to be ; and this we actually find to be the case loith the 
elements taken as a ivhole. This will be again referred to 
farther on, in speaking of Meyer's " Cur^-e of the Elements.-" 
As the tenacity of a metal (or the weight required to break a 
rod of unit cross section) depends on the cohesion* between 
the constituent particles of the metal, we should expect that 
those metals which have the highest melting-points would also 
be the most tenacious ; and this is really the case. Metals 
like Fe and Cu, which melt at comparatively high tempera- 
tures, have a far greater tenacity than such metals as Zn, PI, 
Sn, which have but little tenacity. 

We have thus endeavoured to show how many of the physical 
properties of the elements are interconnected with one another. 

One of the chief objects of the chemist and physicist of the 
present day is to refer all the properties of the elements, both 
chemical and physical, to as few, what we may call, standard 
2)}'operties as possible, till finally one standard property is ob- 
tained, to which all the others may be referred in some way 
or other ; or, in other words, ive have finally to choose some 
standard property, of ivhich all the others are a function, so 
that when we are able to explain this standard property we 
shall at the same time be able to arrive at the cause of the 
other properties, and thus be in a condition to j^redict the 
nature and degree of the properties of any given unknown 
element, or any unknown properties of a known element, of 
which the standard property has been determined numerically. 

Now, whenever possible, we should select as our standard 
properties those which can be represented numerically, as the 
atomic weight, specific gravity, melting-point, boiling-point, 
&c.; and then of these take as our final standard property that 
which can be determined and represented numerically in the 
most exact manner, and which is subject to least variation with 
external circumstances. Thus, we mioht take as our ultimate 

• • IIP 

standard the coefficient of expansion, since this is capable or 
pretty exact determination ; but it would not be advisable to 
do so, as it is liable to great variation with the physical con- 
dition of the body. The tendency at present (and it is no 
doubt the right tendency) is to take the atomic Aveight as the 
ultimate standard, and refer all the other properties to it ; for 
it is capable in most cases of very exact determination, as Stas's 

* Molir lias recently sliown tliat cohesion is but one form of clieuiical 
affinity, Liebig's ^n«. cxcvi. p. 183, 

Phil. Mag. S. 5. Vol. 8. No. 49. Oct. 1879. Y 

310 Dr. T. Carnelley on the 

classical researches have shown, and for a given clement is, as 
far as wo know, absolutely invariable. 

This subject (viz. the reference of the properties of the ele- 
ments to their atomic weights) was first attacked in a syste- 
matic manner by Newlands ("' Law of Octaves," Chem. News, 
xiii. p. 113, also ibid. x. pp. 59, 194), who in 1864 pointed 
out that tlu! atomic weights and properties of the elements 
vary periodically with one another ; and in 1809 Mendeljetf, 
apparently independently of Newlands, in an elaborate and 
most important paper, propounded what is known as the 
Periodic Law {Uent. c/iem. Ges. Ber. ii. p. 553, Ann. Chem. 
Pharm. Suppl. viii. pp. 133-229). This law states that 
" The properties of the elements arc a periodic function of their 
atomic locights.^'' What Mendeljetf in reality did was to take the 
atomic weight as his final standard, and represent each of the 
other properties as a function of this standard. Mendeljeff 's 
researches refer chiefly to the relations between the atomic 
weights and properties of the elements ; and before going on 
to the question of compounds, we shall direct attention to some 
of the more salient features of his work. He points out that 
if the elements be arranged according to the size of their 
atomic weights from H = 1 to U = 240, then the relations be- 
tween their atomic weights and their chemical and physical 
properties exhibit a periodic function. As an example, take 
those elements the atomic weights of which lie between 7 and 
36, thus : — 
Li =7 Be = 9-2 B =11 C =12 N = 14 = 1G F =19 
Na = 23 Mg = 24 Al = 274 Si=28 P=31 S=32 Cl=35-5 

Here the elements up to F are arranged in the first line and 
those after F in the second line, each element as it comes 
being placed immediately under the one above. It is readily 
seen that those elements which stand in the same vertical 
column have very similar properties, and are in fact always 
classed as belonging to the same family or group. It is there- 
fore evident that the character of these elements changes 
regularly and gradually with the increase in their atomic 
weights ; and that this variation is a periodic one, i. e. varies 
in the two series in a similar manner. As a further example 
of this, take the composition of the oxides of the above four- 
teen elements, and it will be seen that the corresponding 
members of both series form oxides having a similar composi- 
tion ; thus : — 

LLO ' BeO B,03 CO, N^O, 00, (ozone) F,0(?) 
Na,0 MgO AUO., SiO, P,03 SO, Cl",0 

This shows also that those elements in the same vertical 
column have the same atomicity, and that the atomicity in- 
creases regularly up to the middle member of each series and 

influence of Atomic Weight. 311 

"then diminishes in like manner. As a still further illustration 
of this, MenJeljeff cites the hydrogen-compounds of these ele- 
ments as far as they are known ; thus : — 

BH3*(?) CH^ NH3 OH2 FH 


Not only does the number of H-atoms vary regularly with 
the atomic weight, but the stability of these hydrogen-com- 
pounds under the influence of different agents, as well as their 
acid characters, and, in fact, all their properties, do likewise. 
Thus HCl is a powerful and very stable acid ; H2 S is a weak 
acid and easily decomposed by heat; in PH3 the acid characters 
are entirely lost and the stability very much diminished, and 
this still more so in SiH4. The physical properties also of 
these elements vary periodically Avith their atomic weight, as 
in the case of the atomic volumes, which are as follows : — 

Li =11-9 Be = 4-4 B = 41 C = SG N= ? 0=? F = 

Na = 240 Mg = 140 Al = 100 Si = 110 P = 16-0 S=16-0 Cl=270 

The atomic volume diminishes from the beginning to about 
the middle of each series, and then increases to the end of the 

Such relations as have been described above apply not only 
to the fourteen elements which have been taken in illustration, 
but to all elements, as will be seen on consulting the following 
Table (p. 312), in which the elements are arranged in the order 
of their atomic weights. 

This Table shows that the properties of the elements first 
change gradually with increasing atomic weight, and then on 
arriving at a certain point repeat themselves in a new series of 
elements or a new j^criod. The change which takes place in 
the atomicity as the atomic weight increases is a very good 
example of this. The atomicity either increases up to the 
middle member of each series, and then diminishes regularly 
to the end, after which it begins to increase again in exactly 
the same way in the next series ; or it continues to increase 
from the first to the last member of the series and then sud- 
denly falls to unity on commencing with the next series. 
These facts are rendered evident by the numbers in the second 
horizontal line of the Table. 

Again, those elements in the same vertical column belong 
to the same family or r/ronjy, and of these groups there are 
eight ; whilst those elements in the scone horizontal line belong 
to the same series, and these series are at present twelve in 
number. On comparing the elements in any one group, we 
at once find that they are in each group divisible into two 
suhgroiqjs — and that in such a way that those members of the 
group belonging to even series are very nearly related to one 
* Francis Jones, Cliem. Soc. Journ. 1879, p. 41. 


Dr. T. Camolley on the 







o S 



J- >' 




.h 00 














o II II 

a> o 



;2; Pi > 



C5 00 

1 i 



CO oo 

►ij ft 


ci ■'^ 

^1 2 




II '^^ 

^ II 












—1 Oi 

11 i- c<i 

■^3 ^ 



'^ s -^ 


^ ^ 

.-H c-i CO 



o o -< 

«« o ® 

*^ u-^ 

•'O^ S 



P.^ MM 

to this 
rees wit 
es from 

tij be - .a 

is a 

3 TJ oT'-S 

Ol S a ja 

Ph-m to ^ 

<s 6 .= .. 

^ " 1 •? 

" W- S cS 

p., « U) 

^ o ':;2 o 

k! -iJ<^ya 

-^ 0-3 

C5 be I, Q) 

Lr"S 3 o- 

00 Sts « 
1— 1 t> ^- t> 

»-"? = 

S "^ fe: ?; . 
-« *" S S • 


•»^ I'- <^-i 

' *^ " -■ rf 

*2 . ej • ^ 

li 3 == s-1 
S -s ."S ""^ ^ 

= PCI :s vT o 
g . .£ ft; ^ 

^ S tc j^ ^ 

^ S 3 5i ,a 
c ^ P- -^ tR 

a) t, o o t. 
* -1- o - S 

Influence of Atomic Weight. 313 

another, and those belonging to odd series also bear great 
resemblance to one another ; whereas the corresponding mem- 
bers of even and of the following nneven series, though they 
have many points of resemblance, yet differ from one another 
in character much more than the corresponding members of 
two even or two uneven series. Thus, in group II,, Ca, Sr, 
and Ba are nearly related, and also Mg, Zn, and Cd ; but Ca, 
though in many respects it resembles Zn, j-et it differs from it 
far more than it does from Sr or Ba. This theory of odd and 
even members of a group is well illustrated by the degree of 
reducibilitv of the elements to the free state, — those elements 
(as Ca, Sr,' Ba, Ti, Zr, V, Cr, Mn, Ta, Nb, W, B, Be, c*cc.) be- 
longing to even series being obtained in the free state with 
comparative difficulty, whereas elements belonging to odd 
series, as Cu, Ag, Au, Zn, Cd, Hg, Tl, Ir, Sr, Pd,"Sn, Bi, tfcc, 
are easily reducible. I also hope to show shortly that all ele- 
ments belonging to even series are paramacinetic, whilst those 
belonging to odd series are diamognetic. We must therefore 
distinguish between Series and Groups, and between the even 
and odd members of a group. 

We have also to distinguish between a long period and a 
sliort period. A short period contains but seven members ; 
thus from Li to F and from Xa to CI form two short periods. 
A long period, on the other hand, embraces seventeen mem- 
bers : thus from K to Br and from Eb to I form two long 
periods ; for we have to pass from K over sixteen elements 
before we come to one, viz. Cs, in which the properties of K 
are more or less repeated, whereas starting from Li, we have 
but to pass over six elements before Ave come to Na, or a point 
at which the properties of Li are in some measure repeated. 

Another point to be noticed is that the last or seventh mem- 
ber of an odd series, as CI, is very different, and in fact oppo- 
site in properties to the first member of the next even series, 
as K ; whereas the seventh member of an even series, as Mn, 
has in many respects considerable resemblance to the first 
member of the next odd series, as Cu. Also in between the 
seventh member of an even series and the first member of the 
next odd series we have a somewhat peculiar group, viz. the 
eighth, in which there are three (or four) elements in each even 
series ; and these elements stand midway in their chemical 
and physical properties between the preceding member of the 
seventh group and the first member of the next series. In other 
words, there appears to be an abrupt change to exactly oppo- 
site properties as we pass from the end of an odd series to the 
beginning of the following even series, as from CI to K, Br 
to Eb, (fcc. ; whereas we pass gradualli/ from the seventh to the 
eighth groups of an even series, and thence to the first mem- 
bers of the followinof odd series. 


Dr. T. Carnelley on the 

This eiglitli group, as previously remarked, is a very peculiar 
group. The elements belonging to it resemble one another in 
many respects ; thus : — (1) they are all of a grey colour and 
are difhcult of fusion ; (2) they possess in a high degree tlio 
power of condensing and giving passage to gases, as in the 
case of Pd, Pt, Fe, &c.; (3) their highest oxides are bases or 
acids of little energ}', and are easily reducible to lower oxides, 
which are far more basic ; (4) their salts form stable com- 
pounds with ammonia &c. 

Atom Anahnmes. — From what has been said above, it will 
be seen that the position of an element II in the system of 
elements is determined by the series and group to which the 
element H belongs, and therefore by the elements X and Y 
standing on either side of it in the same series, and also by the 
elements W and W standing above and below it in the same 
subgroup — thus, 


series :- 




and this in such a way that the properties of R are the mean 
of those of X, Y, R', and R''. The elements X, Y, R', R'' 
are termed by MendeljefFthe atom analogues of the element R. 

Group VI. 

I S 

Series 5: — As 




Here As, Br, S, and Te are the atom analogues of Se- the 

atomic weight of which is equal to the mean of those of the 

,, „ , , ,, 75 + 80 + 32 + 128 ^„ ^ , 

otneriour elements ; thus ^ = iv. bo much, 

then, for the influence of the atomic weights of the elements 
on their chemical properties. We shall now endeavour to 
point out this influence on the physical properties ; and for the 
sake of illustration we will take the melting-points, as they are 
capable of being represented numerically. In the following 
Table the elements are arranged exactly as in Mendeljeft''s 
original Table (vide supra), the only dift'erence being that the 
atomic weights are replaced, where possible, by the corre- 
sponding melting-points. 

Influence of Atomic Weight. 





X. — c-i 

S2 ^;^^ 


li II i" 



II 11 










— — 



~ i£ 




~ 5 






OOtr = CO ^ = 

'P-nS. -^ § DO -s r^ . 







s ^ 








CV. ^ jv, 

ii IT .!! 

;^ i=! ft 


= a 


£ o 

«0 ^ = CO x 











J^ " 





Dr. T. Carnellev on tlifi 

Tliis T;il)lo sliows lliat if llie elements be taken in the order 
of their atomic weights there are, Avith but very few excep- 
tions, no sudden jumps from a high to a low melting-point, 
or vice versa, Avhiist the end of one series of elements runs 
gradually into the beginning of the next. Thus we pass by a 
series of gradations from easily fusible sodium to almost infu- 
sible silicon, and thence ou to gaseous chlorine, then to easily 
fusible potassium, &c. This running of the end of one series 
into the beginning of the next is especially seen in the case of 
group VIII. ; and it is worthy of note that a similar thing 
occurs with the heat of formation of the dichlorides, and also 
with the atomic magnetism of the same metals *, which latter 
has recently been determined by Wiedemann (Phil. Mag. [5], 
vol. iv. pp. 161, 276), thus: — 




Co. Ni. 


Zn. , Ga. 

Melting-point a. 2270 
Heat of for-| 

mation of 


Atomic mag-l 

iietism 1 













The above remarks will be quite sufficient to show that this 
Periodic Law is a truly scientitic one, and not a mere nume- 
rical curiosity ; for it opens up new analogies, and therefore 
points out new paths for the investigation of the elements. 

Niivierical Bclations heticecn the Atomic Weit^hts of the Klc- 
ments. — Some interesting and curious 7iz/7??mc«/relatiojis like- 
wise exist between the atomic weights of the elements, of which 
the following may bo taken as examjiles. 

(1) The atomic weights of the elements of the first group 
are simple multijiles of 7'7, thus : — 




Li ... 

7-7 X 1= 77 


Na ... 

7-7 X 3= 231 



7-7 X r)= 38-5 

39 1 


7-7 X 8= 61-6 



7-7x11= 84-7 


Ag ... 

7-7x14--= 107-8 


Cs ... 

7-7x17 = 130-9 




7-7x20 = 1540 


Calculated from the atomic weights of its 




.. .. 1. 


7-7x26 = 200 2 


Ought to be 199 according to Mendeljeff. 

Here the multipliers of 7*7, with the exception of those for 
Li, Na, and K, form an arithmetical series with the common dif- 
ference 3, whilst between Li and Na, Na and K the common 

* This was first pointed out by the author in a paper read before the 
Royal Society, June 10th, 1879 (Proc. Roy. See. No. 197, 1879). 

Influence of Atomic Weight. 


difference is 2. Now it is remarkable that this difference of 
2, instead of 3, for Li and Xa likewise has its influence on the 
properties of these elements and those belonging to the same 
series ; for, as Mendeljeff has pointed out, his second series of 
elements, containing Li, Be, C, X, 0, and F, and part of his 
third series, containing Xa, Mg, Al, and Si, are apparent ex- 
ceptions to his theory of odd and even series. Thus Xa, 
though belonging to the same subgroup, does not so much 
resemble Cu, Ag, and Au as the latter resemble one another ; 
and the same thing holds good for Mg, F, 0, X, C, <S:c. This 
is rendered especially evident by the melting-points (see 
Table on p. 315), and explains why X 0, F ?, Xa, Mg, Al, and 
Si have melting-points which are so very different from those 
of the other members of their respective subgroups, and re- 
semble more those of the other subgroup. 

(2) Another interesting numerical relation between the 
atomic weights of the elements is that pointed out by Woechter 
{Deut. chem. Ges. Ber. xi. 11). This is represented in the 
f olio win f; Table : — 

TniTalent F =19 

Bivalent O =16 

Trivalent N =14 

Quadrivalent... C =12 

Trivalent j B =11 

Bivalent I Be = 9-2 

Univalent ! Li = 7 


Ca = 40 
K -391 

a+(4xl6). 'a+(5xl6). a+(6xl6). a+(7xl6) 

Br =80 

Se =79 

As = 75 


Sr =87-5 

I =127 

Te = 12S 
Sb = 112 


Ce = 140 
Di = 138 

This Table exhibits the following relations : — 

(a) TliB a/ffinitij of the elements climinisJies from F to Si icith 
rising atomic weight and rising atomicity ; and then from this point 
up to Cs it increases icith rising atomic weight and falling cdonnciti/. 

We have therefore F at the beginning and Cs at the end 
of the series : and these two elements have the strongest, but 
opposite, affinities. The other elements have a smaller affi- 
nity the nearer they stand to the middle of the series. This 
middle point is marked in the Table by the number 76 in 
large type. In other words, as we pass from F, the most ne- 
gative of the elements, they tend to become less negative and 
more positive till we reach Cs, the most positive of all. 

These statements are rendered evident by the following 
Table (p. 318) (giveubyWoechterin the memoir referred to), 


Dr. T. Ctirnolloy on the 









c». c^. 3 '*^' **^' ''• •■ 

C»^ CV, CV. cv. C^ 






1 1 



,i5 e^ C^. Cv, c^. C^, ^, CV, cv, CV, 1 11 




1 1 










a) CV. C». CV. cv, o-. 



bS tc ^ >■ 








m = 

1— 1 





Si mo 













» 1 1 1 1 1 

g cv, ei. cv. 1 




3 Q 

1 1 1 1 1 


« g ^ 








- cv. cv. 

£ 2 

2 1 


^ <^ ^ A 

c Q 





1 1 ! 1 1 



cv. cv. a cv. cv. 





1 1 1 1 1 



1 1 

1 1 1 1 1 




c*- cv. e^ cv. 



1 1 1 1 1 1 



6 6 >^ 



1 o g 



« « O 


1 1 1 1 1 


SD »5 


-= ^2 3 a 




f§ rt f^ ^ 





1 J. 


» T » T 


1 ■ ' 

























» ^- 

- C 

5 S( 

2 CC H 12 

; A^ -< M o cc 

Influence of Atomic Weight. 


in which is represented the affinity for H (which may be consi- 
sidered as a highly positive metal in the gaseous state) of the 
various elements from F to Si ; and it is seen that these affi- 
nities diminish from F to Si in such a way that each element is 
capable of decomposing the hydrogen-compounds of all the 
succeeding elements. 

(b) If the statement contained in (a) be true, then the heat 
evolved {for 1 atom CI) in the combination of the dijferent 
elements icith CI to form normal chlorides u-ill increase from F 
to Cs, the heat evolved on the combination of 2 elements 
being a measure of their affinity for one another. This is 
represented in the following Table*: — 








F = ? 

CI = ? 


s = ? 

N = ? 

P =25-2 

C =? 

Si =39-4 

B =361 

Al =52-0 

Be= ? 


Li =94-0 

Na =97-7 

Ca= 84-8 
K =104-6 

Se = ? 
As = 240 

Sr =92-3 

I =? 

Te= ? 

Di= ? 

Cs= ? 

(c) The arithmetical mean of the atomic weights of the tioo 
elements loith equal but opposite afijiities is approximately equal 
fo 76. Thus:— 

F = 19 + Cs = 133 

N=14 + Di=138 

= 76, 

0=16 + Ba=137 

= vb, 

I=:127 + Na = 23 


Te = 128 + Mg = 24 ^^ 
^ — = ^6, 

= 76-5, 

= 75, 

Sl = 122 + Al = 27-4 ^, - 

; = <4-5. 

(d) The melting- and boiling-p)oints of the elements increase 
from F to Si toith rising atomic iveight and rising atomicity; 
and from that qyoint to Cs they diminish icith rising atomic weight 
and falling atomicity. (Compare with Table on p, 315.) 

In his original paper, Woechter shows that similar relations 
hold also as regards the specific heat and specific gravity of 
these elements. 

* The numbers given in tliis Table are chiefly those determined by 
Berthelot and Thomsen, and were not given in Woechter's original paper. 

320 Dr. T. Carnelloy on the 

W. C. Williams and T. Carnelley (Chem. Journ. lf^7!», 
p. 563) have shown that a curious relation (whether accidental 
or not it is inij)ossible to say) exists between the melting- and 
the boiling-points of CI, 13r, I, and of S, Se, and Te. The 
melting-points of the latter elements are respectively twice 
and the boiling-jioints three times as high as those of the Hrst- 
named elements, all being reckoned from the absolute zero 
(-273°), thus:— 


CI = 198 X 2 = 3P6 (Bcrthclot) S = 388 (Person). 

Br = 248x2 = 490 (Baiinibauer)* Se = 490 (Hittorf). 

I = 387 X 2 = 774 (Stas) Te = 773 ( Watts's Dictionary). 

Cl= 240x3= 720 (Eeguault) S =720 (Eegnault). 

^'•={331x3= 993(Sd;is)} Se = 953 (Williams and Carnelley). 

I = 473x3=1419 (Stas) Te boils below 1G60, since Devillc and 

Troost took the vajioiir-density of 
Te at this temperature. 

The melting-point of I is equal to that of S, and double thai 
of CI. That of Te is double that of S. Similar relations also 
hold in the case of the boiling-points, except that the boiling- 
point of I is two thirds instead of equal to that of S. If the 
boiling-point of I be twice that of CI ( = 240° x 2 = 480°), then 
the number 473 is 7° too low ; but Stas gives the boiling- 
point of I as slightly above (473 — 273 = 200°), thus confirm- 
ing the calculated number. 

Applications of the Periodic Late. — MendeljefF has pointed 
out several important applications of the periodic law, of which 
the following are the more important : — 

(1) To the Classification of tlie Elements. — This is in fact 
the only scientific and natural classification ; for it is the 
only one which takes into account not only the chemical pro- 
perties and atomicity, but likewise the physical properties and 
atomic w'eights. 

(2) To tlte Determination of the Atomic Weights of Rare 
Elements. — This will be best explained if we take an ex- 
ample in illustration, such as indium. Having found the 
equivalent of the element ( = 37-G), we calculate what its 
atomic weight would be supposing it were a monad, dyad, 
triad, and tetrad resj)ectively, and we obtain the following 
results : — 

]Monad. Pvad. Triad. Tetrad. 

Atomic weight= 37-G 75-2 112-8 150-4 
Now it cannot be a monad, because there is no vacant place 

• Baumhaiier states {Dent, clietn. Ges. Ber. iv. p. 927) that Br always 
elves a melting-point Uvo or three degrees too high if it is not perfectly 

Influence of Atomic Weight. 


in the Table of atomic weights (p. 312) corresponding to a 
monad with atomic weight approximating to 37-G, for they 
are already occupied by K and CI. For similar reasons it 
cannot be a dyad ; it must therefore be either a triad, and 
belong to group III., or a tetrad and belong to group lY, 
But in the latter case its atomic weight ought, accordinor to 
the mean of the atomic weights of the atom-analogues of a 
tetrad position, to be either 140 or 164, and not 150*4 ; whilst 
its properties and those of its compounds ought to resemble 
either those of Sn and Pb or those of Zr and Th ; but this is 
not the case. Consequently there only remains the triad po- 
sition in group III. and atomic weight 113. 

(3) To the Determination of the Properties of still undisco- 
vered Elements. — The Table of elements (p. 312) shows that there 
are still many vacant places to be filled by elements yet to be 
discovered. But from what has been already said, it is easily 
seen that the periodic law renders it possible to predict, within 
certain limits, the properties of still undiscovered elements 
when those of their atom-analogues are known. 

At the time when Mendeljetf published his memoir, the 
position between Al and In was still unoccupied ; and from 
the properties of the atom-analogues of that position, viz. Al, 
In, and Zn, he made predictions as to the properties of the 
missing element. This then unknown element he termed 
eka-aluminum. Since that time gallium has been discovered, 
and its properties described by Lecocq de Boisbaudran, from 
which properties it appears that it is the missing element eka- 
aluminium. In order to show, therefore, the extent to which 
the predictions of MeudeljefF have been verified, the predicted 
and the actual properties of gallium are placed side by side in 
the following Table*: — 

Predicied Properties. 

(1) Atomic weight =1)8. 

(2) Specific gra-vitj = 59. 

(3) Easily fusible. 

(4) It5 chloride will be volatile. 


(5) Will be easily obtained iu 
metallic state. 

(6) Its sulphide will be insoluble in 

(7) Will be discovered by the spectro- 

(8) Precipitated bjBaCOg in the cold. 

(9) Oxide soluble in ammonia. 
(10) Will form an alum. 

Actual Properties. 

(1) Atomic weight =09 8. 

(2) Specific gravity =5-956. 

(3) Melts at 30= C. 

(4) Gallium chloride is easily fusible 
(melting-point 73" C.) and volatile. 

(5) Can be easily obtained in the me- 
tallic state. 

(0) Graliium sidphide is insoluble in 

(7) Discovered by spectroscope, giving 
characteristic violet bands. 

(8) Precipitated by BaCOg in the cold. 

(9) Oxide partially soluble in ammonia. 
(10) Forms an alum. 

(4) To the Correction of those Atomic Weights which are 
* See also a paper by Muir (Phil. Mag. April 1877). 

322 Dr. T. Curnelloy on the 

someiuhat itncertain. — As a case in point, wc have uranium, to 
Avliich the atomic weit^ht 120 was. formerly assigned. Mcn- 
deljetl", however, pointed out in his oriffinal memoir that the 
true atomic weight of this element ought to be 240 ; and this 
number is noAV generally adopted. 

(5) To the Completion of our Knoidedge of the Conibination 
forms of Chemical Compoiinds. 

Meyer's Curve of the Elements. — In December 1869, shortly 
after Mendeljeff proposed his periodic law, Lothar Meyer 
])ublished a very interesting article in Liebig's Annalen " On 
the Nature of the Chemical Elements as a Function of their 
Atomic Weights," in which he showed that by taking the 
atomic weights as abscissaj and the corresponding atomic 
volumes as ordinates, a curve is obtained which is a visible re- 
presentation of the fact that not only the atomic volume, but 
also all the properties of the elements are a periodic function 
of their atomic weights. As the atomic weight increases, the 
atomic volume increases and decreases regularly in such a way 
that the curve which represents these periodic changes is 
divided by 5 maxima into 6 divisions, each of Avhich has the 
form of a suspended chain. Of these divisions, the 2nd and 
ord, and likewise the 4tli and 5th, are very similar to one 
another, and are of nearly equal dimensions. The Gth divi- 
sion is at present incomplete. The 2nd and 3rd divisions cor- 
respond to Mendeljeff's short periods, viz. Li to F and Na to 
CI, and the 4th and 5th divisions to two of his long periods, 
viz. K to Br, and Rb to I. 

As a general rule, those elements standing in correspond- 
ing parts of the curve have similar properties. In divisions 
2 and 3 the atomicity increases regularly as we pass from left 
to right down the curve till we come to the lowest point, 
where the atomicity attains a maximum; and then, on rising up 
on the opposite side of the curve, the atomicity gradually de- 
creases again till it becomes unity. In the other divisions of 
the curve the atomicity increases as we pass down the curve 
from left to right, but in this case comes to a maximum half- 
way down the curve, after which it decreases again, and attains 
a minimum at about the lowest point ; and then as the curve 
rises again, the atomicity undergoes exactly the same changes 
as it did on the falling portions of the curve. Metals which 
are easily expanded by heat lie at or near the maxima, whilst 
those with a small coethcient of expansion stand at or near the 
minima. Heavy brittle metals occur just before the minima 
on the falling portions of the curve. All those elements which 
occur on the rising portions of the curve are brittle non- 
metallic elements. 

Influence of Atomic Weiylit. 323 

In divisions 2 and 3 the elements on the falling portions of 
the curve are electro-positive and cloetro-negativo > n the 
rising parts, whilst in divisions 4, 5, and 6 those elements 
following directly after the maxima and minima are positive, 
and those occurring immediately before these points are nega- 
tive. A icell-inarkecl jDositive or negative character is possessed 
only by those metals which have comparatively large atomic 
volumes, or, according to Meyer, '' the aggregation of a large 
mass in a small space appears to be incompatible with the 
development of a marked positive or negative character." 

On comparing the Table of melting-points (p. 315) with 
Meyer's curve of the elements, we tind that the melting- 
points (and also the boiling-points) rise and fall as the curve 
falls and rises; i. e. they are inversely as the atomic volumes*. 
The only important exceptions to this rule are As and Se in 
series 5, Sn, Sb, and Te in series 7, and Tl, Pb, and Bi in 
series 11, the melting-points of which are too high to be in 
accordance with the above rule. I have pointed out {Deut. 
chem. Ges. Ber. xii. 440), as previously mentioned, that the 
coefficients of expansion of the elements are the greater the 
lower their melting-points, and that there are but five excep- 
tions to this rule, viz. As, Sb, Bi, Te, and Sn. Now it is seen 
that all these five elements are also among the eight excep- 
tions to the relation betA\een the melting-point and atomic 
volume, as is shown in following the course of Meyer's curve. 
All these eight exceptions likewise belong to odd series and 
follow one another directly in their respective series. A fur- 
ther inspection of Mej-er's curve shows that it rises regularly 
and somewhat sharply from Ni, Cu, and Zn to Ga, and then, 
though it does not really do so, yet it shows a very strong ten- 
dency to turn downwards to As. In the same way, in division 
5 the curve rises regularly and rapidly from Pd, Ag, and Cd 
to In, and then exhibits a strong downward tendency towards 
Sn and Sb. These facts may perhaps serve to explain why the 
melting-points of the elements As, Se and Sn, Sb, Te at 
these points on the curve are not regular either in relation to 
the atomic volume or to their coefficients of expansion. The 
same thing applies also in the case of Pb. Therefore, though 
at first sight these exceptions appear to contradict, yet a closer 
inspection shows that they rather confirm the course of Meyer's 

* This is only what we might expect from the remarks on p. 308 -v^ith 
regard to Beltone's experiments. For since, according to him, the hard- 
ness of an element = — -. =- and since the harder a bodv, the hio-her 

atomic vol.' "' ° 

its melting-point, then the gi*eater the atomic vol. of an element, the more 
easilv fusible it is. 

324 Prof. F. Rosetti's E.rperimental Researches 

curve, its (lo^^Tl^vard tendoncy at the points referred to being 
merely the expression of the facts. 

By takino; the atomic weights of the elements as abscissae 
and the reciprocals of the corresj)onding melting-points Jis 
ordinates, a curve is obtained Avhich lias a form similar to that 
of Meyer's (in which the ordinates represent the atomic 
volumes); for, as in the latter, we have at the maxima the 
halogens and alkali-metals, and at the minima C, Si, Ti, Mn, 
Zr, rt, ami allied elements. 

Mechanical Arrangement of the Elements. — If the elements 
are arranged in the order of their atomic weiffhts so that the 
first member of each horizontal series follows directly after 
the last member of the preceding series, B after Be, Al aft?r 
Mg, &c., and if, Avith Lothar Meyer (^Die modernen Theorien tier 
Chemle, p. 301, 2nd edition), we imagine that the Table is 
rolled round a perpendicular cylinder in such a way that the 
group beginning with B and Al joins on to that of the alka- 
line-earth-metals Ba, Mg, Ca, &c, then we obtain, as is readily 
seen, a continuous series of all the elements arranged in a 
spiral according to the size of their atomic weights. Those 
elements which in this arrangement stand directly under one 
another on the cylinder belong to the same group. It is thus 
evident that bv arran^rino- the elements in this mechanical 
manner we obtain a truly natural scientific classification. 
[To be continued.] 

XXXVII. E.rperimental Researches on the Temperature of the 
Sun. By F. RosETTi, Professor of Phyf<ics in the University 
of Padua* . 

THE question of the effective temperature of the sun has 
been keenly discussed of late years, although as yet with- 
out any definite result. Newton was the first to attack this 
problem ; it Avas afterwards studied by Saussure, and more 
recently by Pouillct, Waterston, Secchi, Erlcson, Yicaire, 
Violle, Crova, and others. 

Although the observations on radiation made by these in- 
vestigators Avere tolerably concordant, the conclusions at Avhicli 
they arrived as regards the temperature of the sun are Avidely 
different. Thus Newton, AVaterston, Ericson, and Secchi 
aflirm that the temperature of the sun cannot be less than from 
one to tAvo million degrees ; on the other hand, Pouillet, Vicaire, 
Violle, and others maintain that it is not above 1500°, or at the 
very most 2500°. 

* Translated from tbe Ann. ilc Chim. ct de Phys, I. xvi. (,1879) by John 
I. AVatt3, Owens College. 

on the Temperature of the Sun. 325 

In 1876 the French Academy of Sciences offered a prize 
for the best solution of the question ; but although, at the ter- 
mination of the competition, a prize was awarded to M. Violle, 
and encouragements to MM. Vicaire and Crova, the Com- 
mission of the Academy declared that the problem had not 
been solved *. The Commission pointed out that the chief 
source of error was the necessity of making use of an un- 
trustworthy extrapolation in order to deduce the solar constant 
to the limits of our atmosphere, and that even this was not 
the least danger which necessarily follows from extending a 
law of radiation, which is hardly applicable to temperatures 
between 0° and 300°, to temperatures above the melting-point 
of platinum. Thus, from almost identical observations on 
solar radiation, Secchi obtained over 2,000,000° by dedu- 
cing the temperature from Newton's formula, whilst M. Violle 
obtained only 1500° by employing that of Dulong and Petit ; 
nevertheless it has been shown that both the formulae are only 
applicable when there is only a very small difference between 
the temperature of the hot body which radiates and that of the 
cold body which is warmed by the radiation. When the two 
formulas are applied to the case of a body rendered incandes- 
cent by the oxyhydrogen blowpipe, the temperature of which 
is certainly as high as 2000°, Newton^s gives 45,900°, which is 
excessively high, whilst that of Dulong and Petit gives 870°, 
which is certainly too low. M. Violle, in order to justify the 
low value given by Dulong and Petit's formula, attributes the 
error to the emissive power of the incandescent body ; and, 
assuming the formula to be exact and applicable even in this 
case, he deduces from it an exceedingly small value for the 
emissive power. 

It appears to me that, instead of forcing the formulse to show 
what they can never do, it would be much better to confront the 
question directly, and, by means of well-chosen experiments, 
to ascertain the law according to which the intensity of radia- 
tion varies when the temperature changes, to determine the 
emissive power of the bodies on which the experiments are 
made and under the conditions in which they are at the time 
of the experiment, and, after having established the formula 
which expresses the radiation within the limits of the expe- 
riments which have served to fix it, to determine exactly 
whether it is applicable to the cases of higher and well-known 
temperatures. It is only when this correspondence exists that 
the use of the formula can be further extended, and the tem- 
peratures of inaccessible and exceedingly hot bodies like the 

* Comptes Rendits, vol, Ixxxvi. p. 813 (1877). 

Phil. Mag. S. 5. Vol. 8. No. 49. Oct. 1879. Z 

326 Prof, F. Rosetti's Experimental Researches 

sun investigated with any degree of accuracy. In so doing I 
hope to overcome one of the chief difficulties which the prohlem 
presents. Like my predecessors, I have been obliged to have 
recourse to an extra]wlation in order to obtain the value of 
the solar constant within the limits of our atmosphere ; but the 
method which I have followed renders it much more precise, 
and I think that the numbers which I have obtained represent 
the temperature of the sun in a satisfactory manner. This will 
be rendered evident by a perusal of the present memoir. 

I. Description of the Instruments employed in the Researches. 

1st, Thermoelectric Piles. — In my experiments I have used 
two piles — one made by M. Duboscq, and the other by M. 

The one made by M. Duboscq (No. 1) w\as composed of 
25 antimony-bismuth elements arranged in the form of a 
straight prism with a square base ; the junctures of the metals 
were placed at the base of the prism, and were covered with 
lampblack. The first rod of bismuth and the last of antimony 
were in communication with two insulated coils of wire in which 
the rheophors were fixed. The pile was protected by a small 
brass case with double wall (fig. 1) in which were two apertures 

opposite to two sides of the pile. The pile was situated in 
the centre of the case and was kept in position by a piece of 

rni the Temperature of the Sun. 327 

metal, C. The case was in the form of a straight prism with 
a rectangular base. Each base, back and front, was mo- 
vable, and had in its centre a window, which admitted the rays 
as far as the junctures in the pile. These windows could, how- 
ever, be closed by double shutters working in horizontal 
grooves set in the outer wall of the case. The interior walls 
of the case were covered with lampblack ; they could not, 
however, radiate towards the faces of the pile, because the 
latter were protected by two tubes E E, E E (rectangular in 
section), which were slightly divergent towards the exterior 
and reached nearly as far as the windows of the case. The 
case with the pile could be inclined more or less to the horizon 
by means of a toothed pinion, G, worked by a rack, F, fixed 
on the case. This rack was supported by a pillar, H, which 
was movable along a divided scale, T, and could be fixed in 
any convenient position by means of a clamp-screw. The pile 
could thus be moved in two directions — one along a horizontal 
line, the other about a horizontal axis. A third movement, of 
rotation about a vertical axis, could be obtained by turning the 
foot L by hand. For the purpose of accurately arranging the 
pile so that its two faces should be perpendicular to the rays, 
two sights (e and/) were fixed to the top of the case. The 
line passing through two holes made in these sights was parallel 
to the longitudinal axis of the pile. In employing solar ra- 
diation, it was certain that the faces of the pile were perpendi- 
cular to the rajs of the sun when the pencil of light which 
passed through the hole in the front sight fell on the hole 
in the hinder one. 

The thermoelectric pile made by M. Grourjeon (No. 2) was 
only used in a few special researches. It was composed of a 
great number of bismuth-antimony elements arranged in the 
form of a straight cylinder with a circular base. It was more 
sensitive than pile No. 1. 

2nd, Galvanometer. — An excellent Wiedemann's galvano- 
meter measured the electric current generated in the pile 
when exposed to radiation. In this galvanometer the devia- 
tions of the magnet were read by means of a telescope on a 
divided scale situated below the telescope and some distance 
from the needle. The current which deflected the magnet 
traversed a wire which was wrapped on two horizontal bob- 
bins, which were placed on the two sides of the magnetic disk; 
they were insulated from one another, and could be moved 
either backwards or forwards. On each of the bobbins there 
were wound two wires, in order that the instrument might be 
used as a differential galvanometer. I arranged the con- 
nexions so as to make the electric current travel over the two 


328 Prof. F. Rosetti's Exj^eriviental Researches 

wires of the same bobbin in the same direction. Moreover 

the two bobbins were placed as near th(^ maonctized disk as 
i)0ssible ; and in addition 1 j)laced a stroiiijlv maiinetizcd bar 
underneath, for the purpose of neutralizing as completely as 
])Ossible the influence of the earth's magnetism on the disk. 
In this manner the instrument was rendered extremely sensi- 
tive. The telescope (furnished with cross-wires) and the 
divided scale were placed at a distance of 3 metres from the 
galvanometer. The scale was divided into fifths of a centi- 
metre, and by means of the telescope could be read to the 
tenth of a millimetre. When the readings of the variations 
wei-e made, it Avas necessary to pay attention to the differences 
in the position of equilibrium of the disk, due to variation of 
the magnetic declination of the earth ; on this account, before 
passing the current, the division of the scale corresponding to 
the cross-wire of the telescope was noticed ; and this served as 
a starting-point in the elimination of successive variations. 

II. Experimental Determination of the Law of Radiation as a 
function of the Temperature. 

Experiments hetxceen 0° and 300°. — In order to make this 
determination, I took first for radiating body Leslie's cube 
filled with water, which I heated to different temperatures 
by a flame, and finally kept it at the boiling-point. For tem- 
peratures between 100° and 300° I employed an iron cube 
filled with mercury. The cover of this cubical vessel was 
pierced with three holes, through two of which passed the 
stems of two thermometers, each of which was graduated up to 
360° ; through the third the handle of an iron stirrer passed. 
At a short distance from the radiating face of the cube was 
placed a diaphragm with a double wall ; in the centre of each 
wall were circular holes with a diameter slightly less than that 
of the opening in the case containing the pile. This precaution 
was taken to insure that every part of the pile should receive an 
equal amount of heat. The exterior walls of the screen were 
blackened ; and between the pile and the first screen a second, 
also with double sides, was placed with windows slightly larger 
than those in the case. The two screens were placed parallel 
to each other and to the face of the case by means of small 
holes, in the same manner that the pile was directed towards 
a radiating object. The experiments were made with the more 
sensitive pile No. 2, and with no more resistance in the circuit 
than that offered by the pile itself, the rheophors, and the wire 
of the galvanometer. The following Table shows the results 
of the experiments : — 

on the Temperature of the Sun. 


Table I. 
Surrounding temperature 23°*8 C. 

Difference between 

Number of 

Temperature of 

temperature of 

Deviations ob- 

the radiating 

radiating face 

served on the 


and surrounding 
























176 6 



























It should be stated that each experiment was repeated at 
least t^^^ce, and that the necessary precautions were taken to 
keep the temperature constant during the experiment. 

III. Empirical Forvmlce, and the Choice of the one ichich best 
represents the Phenomenon. 

It was important to determine from these experiments the 
law according to which the thermal effect produced by radia- 
tion varies with the temperature of the radiating surface. For 
this purpose I constructed a curve from the preceding Table, 
taking for abscissse the numbers contained in the third column, 
and for ordinates the corresponding numbers of the fourth 
column. A simple inspection of the curve shoAved that the 
thermal effect of the radiation increases much more rapidly 
than the temperature of the I'adiating surface, and therefore 
Newton's law, which is expressed by a straight line, is not ap- 
plicable here. In tact it has long since been shown that New- 
ton's formula is only applicable when there is a small difference 
between the temperature of the radiating body and the body 
which receives the radiation. By a very careful series of ex- 
periments Dulong and Petit proved that the law of radiation 
is represented by the formula 

^ = &(a'-'.-l); 

330 Prof. F. Rosetti's Experimental Researches 

in which q represents the quantity of heat given out by the 
unit surface of the radiating body in the unit of 

t the temperature of the hot body, 

ti the surrounding temperature, 

a and h two constants. 

Although this formula corrrectly represents the phenomenon 
of radiation in the experiments of Dulong and Petit, which 
extended only between the limits of 0° and 280°, yet it has 
been shown by Ericson that it is not applicable when the dif- 
ference in temperature between the radiating body and the 
surrounding temperature exceeds 80°. M. Jamin declares 
that it is an empirical formula which becomes inexact at high 
temperatures. Since, then, the formula of Dulong and Petit 
is empirical and limited in its use, I have sought to substitute 
for it another formula, which more correctly represents the 
radiation as a function of the temperature of the radiating 
body and the temperature of the medium surrounding the cold 
body which becomes warm. After much consideration I have 
decided to adopt the formula 

y = aT{T-e)-h{T-e)', 

in which y represents the thermal effect of the rays, measured 
by the thermoelectric pile ; 

T is the absolute temperature of the radiating body; 

6 is the absolute temperature of the medium in 
which the pile is placed ; 

a and h are two constants to be determined, which 
depend on the nature of the thermoelectric instru- 
ment, and which remain constant for one and the 
same body radiating at all temperatures. 

The first of the two terms may be regarded as representing 
the thermal effect produced by the rays in vacuo ; the second 
represents the influence of the surrounding air. This formula 
is, as regards its form, identical with that of Newton, since 
the value of y is proportional to the difference T— ^; but 
whilst in Newton's formula the emissive power of the radia- 
ting body is considered to be independent of the temperature, 
in the formula proposed by myself the emissive power is re- 
presented by ET- ; that is, it is proportional to the square of 
the absolute temperature of the radiating body. In a body 
with a maximum emissive power, such as lampblack, E should 
be equal to 1 only for T=l ; but as T increases the emissive 
power should also increase, in proportion to the square of the 
temperature. This supposition was confirmed by many of my 

on the Temperature of the Sun. 331 

experiments, and also bj those of Tyndall on the emission of 
heat (see Pogg. Ann. vol. cxxiy ; also Wiillner, Lehrhuch 
der Ph'jsik, vol. iii. pp. 215, 216). The best experiments of 
Melloni and Tyndall have shown that, as the temperature rises, 
the radiation of the body increases, because not only does the 
energy of the rays belonging to the primary undulations in- 
crease, but also new undulations of higher refrangibility are 
added to them. Thus the effect of radiation increases on 
account of the very large number of rays of different refran- 
gibility, and on account of the intensity of each ray. 

In order to ascertain whether the formula properly repre- 
sents the phenomenon of radiation between the limits of my 
experiments, and to iind out whether it is capable of further 
extension, I be^an bv determinino- the value of the constants 
a and h by means of the experimental data of the preceding 
Table. By taking experiments 7 and 10, in the first of which 

y=116-7, T=196-6 + 273=469-6, T-6'=172-8, 
and in the second 

y = 204-0, T=256-6 + 273 = 529-6, T-^ = 232-8, 
I obtained the values 

Ioga=4-5252152-10, rt = 0-00000335131, 
log Z» = 8-8040253 -10, Z/ = 0-0636833. 

In order to make sure whether the formula, with the values 
of a and h calculated in this way, represents the radiation for 
all differences of temperature between 0° and 273°, the values 
of y for intervals of 50° were calculated and compared with 
the corresponding values taken on the curve. 

Table II. 


of tempe- 

observed on 


Ordinates y 

Ordinates v 

the thermo- 


taken from calculated bvi Difference. | 

meter, C. 


the curve. 

the iormiila. 








































I wished to determine to what extent the formula of Dulon g; 
and Petit was capable of representing the effect of radiation 

332 Notices respecting Neio Books. 

between the limits of the experiments made. For this purpose 
the two vahies, 

T-^=130°, to which ?/= 69*9 corresponds, 

T-^=2G0°, „ y=253-5 „ 

were deduced from the curve and introduced into the formula 

In this manner the values 

^=42-9728, log 6=1-6331939, 
rt= 1-00746, loga=0-00322612, 

were obtained for a and h. The following Taljle shows the 
ditferences between the ordinates deduced from the curve and 
the values calculated from the fonnula of Dulong and Petit. 

Table III. 

Difference of 




taken on the 



calculated by 

Dulong and 

Petit's formula. 














-0 95 

Therefore the parabolic formula which I have proposed is 
more suital)le than ihat of Dulong and Petit ; and accordingly 
I have used it in my later experiments. 
[To be continued.] 

XXXYIII. Notices respecting Neio Books. 

MesearcJies on tlie Motion of the Moon, made at the United States Naval 
Observatory, Washinr/ton. By SiMOX Xewcomb. Professor U.S. 
Navy. Part I. Reduction and Discussion of Obsen'ations of the 
Moon before 1750, forming Ajtpendix II. of the IVasJiinyton Ob- 
servations for 1875. "Washington, 1878. 
nPHE object for which this work was undertaken is fully expressed 
-■- in the first paragraph of the author's preface as follows : — " For 
several years after the publication of Hansen's Tables of the Moon 
it was very generally believed that the theory of the motion of that 
body, after having been the subject of astronomical and mathema- 
tical research for two thoiisand years, was at last complete, and that 
in consequence the motion of the moon could now be predicted 

Notices respecting Neio Books. 333 

with the same accuracy as that of the other heavenly bodies. In 
1870 the writer showed that this belief was entirely unfounded, 
and that the correctness of the tables since 1750 had been secured 
only by sacrificing the agreement with observations previous to that 
epoch, so that about 1700 Hansen's tables deviated more widely 

from observations than did those which they superseded 

Altogether it appeared that, notwithstanding the immense improve- 
ment that Hansen had made in the accuracy of the inequalities of 
short period, the theory of those of long period was no nearer such 
a solution as would agree with observation than when it was left 
by Laplace," 

In consequence of Hansen's tables deviating so widely from ob- 
servation in 1700, and generally at epochs previous to 1750, " the 
latter date was fixed upon as the terminal point of the investiga- 
tion, consisting of the study of the inequalities of long period, 
partly because it is the epoch at which accurate meridian observa- 
tions commence, and it is also that which separates the period 
within which -ne have readily accessible observations and copious 
tables of reduction founded on modern data from that during which 
both these requirements are wanting." 

This investigation, as well as that of the mathematical theory of 
the inequalities of long period in the moon's mean motion, were 
made a part of the author's official duty at the Naval Observatory. 
Difficulties arising in the investigation of inequalities of long period, 
it Avas found necessary to leave this part incomplete until the best 
method of treating the subject could be decided on. In the mean- 
time the author, in the course of a journey in Europe, obtained 
several valuable series of observations which he has employed in 
obtainujg his result. He remarks that the material most used has 
hitherto been least known ; also that the most valuable portion of it 
is possibly found in the unpublished Paris observations, whereby the 
moon's mean longitude is determined with astronomical accuracy 
from 1680 onward. 

The general scope of the •n'ork may be gathered from the table of 
contents, as follows : — § 1. Historical Introduction. § 2. Sum- 
mary of Data for determining the apparent Secular Acceleration. 
§ 3. Discussion of Narratives of ancient total Eclipses of the Sun. 
§ 4. The Ptolemaic Eclipses of the Moon recorded in the Almagest. 
§ 5. Arabian observations of Eclipses, from Caussin's translation of 
Ebn Jounis. § 6. Mode of deducing the Errors of the Lunar Ele- 
ments from observations of Eclipses and Occultations. § 7. Eifect 
of Changes in the Lunar Elements upon the path of the central line 
of an Eclipse. § 8. Observations of Bullialdus and Gassendus, 
§ 9. Observations of Hevelius. § 10. Observations by Astrono- 
mers of the French School between 1670 and 1750, from Manu- 
scripts at the Paris and Pulkowa Observatories. § 11. Positions 
of the Moon from Hansen's Tables used in comparing the pi'ece- 
ding observations with, theory. § 12. Details of Eeductiou of the 
Occultations. § 13. Equations of Condition given by the preceding 

334 Intelligence and Miscellaneous Articles. 

Occultations of Stars. § 14, Observations of Eclipses from 1020 
to 1724. § 15. Discussion of Deviations in the Moon's in(>an Mo- 
tion. §10. Motion of the Moon's node. § 17. Concluding llemarks 
on the Value of the Secular Acceleration deduced in this paper. 

For the subjects treated in the sections above enumerated we 
must refer the reader to the work itself, in which will be found 
evidence of the skill with which the author has accomplished his 
task, and the results at Mhich he has arrived. In section 15, de- 
voted to the discussion of Deviations, the author, speaking of the 
cause of outstanding deviations, remarks that we may make two 
hypotheses: — (1) That these deviations are only apparent ones, 
arising from inequalities in the axial rotation of the earth. The 
deviation of the observed secular acceleration from the theoretical 
value G""18 has long been attributed to a retardation of the earth's 
rotation ; and by supposing this retardation to be a variable quan- 
tity, and indeed sometimes to change into an acceleration, we may 
completely account for the observed deviations. (2) We may sup- 
pose the de\ iations to arise from one or more inequalities of long 
period in the actual mean motion of the moon. On the first of 
these hypotheses the author says, " If it is correct, the problem of 
predicting the moon's motion with accuracy through long intervals 
of time must be regarded as hopeless, since it cannot be expected 
that variations in the earth's axial rotation will conform to any de- 
terminable law. Success in tracing the deviations in question to 
the moon itself, and to the theory of gravitation, is therefore a 
consummation to be hoped for." 

In the last section, containing the concluding remarks on the 
value of the secular acceleration deduced by the author, he suggests 
that " either the recently accepted "salue of the acceleration and the 
usual interpretation of the ancient solar eclipses are to be radically 
altered, the eclipse of —556 not having been total at Larissa, and 
that of — 514 not having been total in Asia Minor, or the mean 
motion of the moon is, in the course of centuries, sul)jected to 
changes so wide that it is not possible to assign a definite \alue to 
the secular acceleration. 

An important feature of this book consists of the collection of 
observations of eclipses and occultations (some hitherto unpub- 
lished) used by the author in his investigation. Altogether the 
work forms a valuable addition to the literature of the Lunar 

XXXIX. Intelligence and Miscellaneous Articles. 


T/'ISUAL phenomena are of general interest, and are often de- 

* scribed but seldom explained. The phenomenon in question 

may be seen under the following circumstances. Face the breeze, 

and without winking allow a small raindrop to fall on the surface 

Intelliqence and Miscellaneous Articles. 335 

of the cornea, all the while keeping your gaze fixed on a lamplight 
some hundred feet away. As the raindrop alights on the cornea, 
several rings of light appear to surround the luminous source. The 
rings gradually contract in diameter. Explanation : — In sunshine, 
the moving ring crest of water produced by dropping a pebble 
into a still and shallow pool projects a ring of light on the bottom 
which gradually increases in size. The mo^dng ring crest, by its 
refractive action, produces a hollow cylinder of rays of ever increa- 
sing diameter ; and we see a section of it on the bottom of the pool. 
The raindrop falling on the cornea spreads out on its siu'face in 
several ring crests, and would similarly produce a series of outward 
travelling rings of light were it not for the combined action of the 
refractive media of the eye. Under the influence of these, two 
hollow cones of light are formed within the vitreous humour directly 
upon impact of the raindrop. The fii-st of these has for its base a 
small circular area of the hind surface of the lens ; and its prolon- 
gation, the second cone, has the retina for its base. As any indivi- 
dual ring-crest spreads out on the cornea, the first cone increases 
in size, the common apex advances towards the retina, and con- 
sequently the section of the second cone projected onto the retina 
decreases in size and appears as a contracting ring of hght. — 
Abstract of paper read in Section D, British-Association Meeting, 
Monday, August 2bth. 


Mr. Schwendler said it would be impracticable to read the 
" Pre'cis of Eeport on Electric-Light Experiments" in extenso, since 
it contained too many technicalities which coidd not ea«ilv be 
followed if the paper were read in the manner usual at these 
meetings, and that he therefore would prefer to give verbally a 
short account of his researches and the results obtained. He 
stated that the inquiry originated with General Strachey, who, in 
April 1876, recommended to the Secretary of State that a trial of 
illuminating Indian railway-stations by the electric light should 
be made. In February 1877 Mr. Schwendler was requested to 
institute detailed inquiries, wliich led him to propose that it would 
be advisable to first make some more experiments before a practical 
trial at Indian railway-stations should be attempted. The Board 
of Directors of the East-Indian Eailway Company agreed to this, 
and sanctioned the necessary outlay, whatever it might come to. 

The experiments made at the India Office Stores, London, ter- 
minated on the 1st jS'ovember, 1878. The report, however, could 
not be finished in time before Mr. Schwendler left for India'; and 
he therefore prepared a pre'cis — the paper before the meeting to- 
night. After pointing out the general results obtained, and ex- 
plaining in a brief manner the three principal questions at issue, 

* Eead before the Asiatic Society oth March 1879 (from the Proceed- 
ings for March). Coramimicated by the Author. 

336 Intelligence and Miscellaneons Articles. 

viz. econonv/ of the electric li/jht, ivactlcahiUtii and efficiency of the 
electric liyht for certain iUHrninatiiuj-jiHrjtnses, and best means of 
distribution of the electric li(/ht, Mr. Schwondler proceeded : — 

You all have heard, no doubt, a great deal about the division of 
the electric light. During the last two years this question has been 
before the public almost permanently. This is not to be wondered 
at, if we consider that on the solution of this problem it will ulti- 
mately depend whether the new mode of lighting becomes a success- 
ful aud general rival to the illuminatiou by gas or other combustive 
means. But before entering on the subject, it will be best to for- 
mulate the question definiteh% to avoid any misunderstanding with 
respect to the answer I am about to give. The question is : — A 
given permanent current (C), no matter how produced, does work 
in a closed single circuit of total resistance (R), of which a part (r) 
represents the resistance of one electric arc. This electric arc pro- 
duces an electric light of measured intensity (I). Now, if we 
introduce, instead of one arc, two arcs of resistance )•' and r" and 
measured light-intensities i' and i" respectively, and suppose the 
current to be the same as before, or the E.M.F. and total resis- 
tance in the single circuit the same, then a priori we should con- 
clude that I=?''-|-r" for r=;-'-f-?-". Experiments, however, show 
that this not the case ; i. e. the sum of the measured intensities of 
two small lights is perceptibly smaller than the measured intensity of 
o»e large light ; aud this difference becomes larger aud larger as we 
increase the number of lights produced by the same current, i. e. 
by the same E.M.F. with the same total resistance in circuit. 
This appears at first sight an inconsistency mth the known laws 
of cause and effect. How is it possible that the same current 
through the same resistance should produce more light in one point 
than in two points, although the total amount of AAork done by the 
given and constant current is exactly the same in one point as iu 
two points ? 

That the measured intensity of one light is invariably greater 
than the sum of the measured intensities of n lights, is an uii- 
doubted fact proved by my own experiments very conclusively. 
But we may M'ell ask. What has become of the energy which is 
expended and does not appear as light ? 

A careful analysis of all the physical facts connected with the 
subject will, however, show easily enough how this apparent loss 
of energy is to be accounted for, without reverting to fai'-fetched 
explanations, and without the necessity of making such statements 
as " the division of the electric light is in contradiction to dyna- 
mic principles," or " the laws of nature must be reversed " (what- 
ever that may mean), or "new laws have to be discovered first, 
before a solution of this important problem could be even at- 
tempted," &c. &c., which I have read frequently in scientific or pro- 
fessional journals and newspapers. Statements of this kind a2)pear 
very clever to the uninitiated, and they are exceedingly cheap to 
make ; but they will invariably do an enormous amount of harm 

Intelligence and Miscellaneous Articles. 337 

to the fui'ther progress of au importaut application of the resources 
of nature. 

It will be seen from the foregoing that I have called the light- 
intensity measured intensity. Por if we produce a light by any 
source, it will be at once perceived that not all the light produced 
by that source can be made available for illuminating-piu'poses. 
A part of the total light will be lost for the special purpose of 
illumination, inasmuch as only a part of the total light is in a posi- 
tion to act on the photometer, or, which is the same, on the retina. 
Hence we may say the total light produced by any means consists 
of two parts : the one is lost for illuminating-purposes, and may 
be called internal light ; the other acts on the retina, can be 
measured, and may be called external or measured light. For 
instance, of all the light produced in one electric arc, a considerable 
part is hidden by the electi'odes between which the arc plays, be- 
cause the electrodes have a volume, and moreover the positive elec- 
trode is hollowed-out like a dome, and it is the highest point of that 
dome which contains the most intense light, which is mostly lost. 
How much this loss in each case will be, depends on a variety of cir- 
cumstances. In the first place, all other conditions being the same, 
that loss will increase with the thickness of the electrodes. The 
loss of light will further increase with a decrease of the length of the 
arc. By length of arc is to be understood the distance between 
the highest point of the hollow of the positive electrode and the 
apex of the negative electrode. Hence already in the case of one 
arc, although naturally we have here the longest arc for the given 
current and the given electrodes, the light lost or the internal light 
may represent a considerable portion of the total light produced in 
the arc. 

If we produce two arcs, it will be seen at o)ice that the sum of 
the losses must be greater than the loss in one arc. Hence the 
sum of the measured intensities of two lights must also be smaller 
than the measured intensity of one light. Suppose the length of 
one arc, when a given current passes, is 3 mm., then the sum of 
the lengths of two arcs will not be 3 mm. but much less, in order 
to have the same current passing through the two arcs as passed 
before through one. From this it follows that the loss of light 
must increase rapidly with the number of lights, and moreover that 
soon a limit for the possible practical division of . the electric light 
is reached, leaving out the question of economy altogether. 

This constitutes one of the reasons why the division of the elec- 
tric light becomes less and less economical with increase of the 
number of lights, and that soon a practical limit will be reached for 
the division. 

To express this result more definitely, we may say : — 

The consumption of power per unit of measured or external light 
is a function increasing with the number of lights produced by a 
given current in a single circuit — supposing, of course, always that 
the sum of resistances of the n arcs is equal to the resistance of 

338 Intelligence and Miscellaneous Articles. 

one are, and tliat tlie other resistance in the circuit, in which no 
light is produced, has remained constant throughout. 

If we had a material infinitely conducting, of infinite strength, 
and with a melting point at least as high as that of carbon, then 
surely the division of the light would be perfectly economical up to 
any limit, inasmuch as we might then use linear electrodes. 

In practice we can only try to approach this limit. Up to the 
present time there appears to be no better material for electrodes 
than carbon, either natural or artificial. But this is no reason why 
au effort should not be made to try to find a material for electrodes 
more accommodating to the division of the electric light than even 
carbon. The above, limited strength, limited electric conductivity, 
and limited melting-point of the material of electrodes, constitute 
only one of the difhculties which stand in the way of an unlimited 
economical division of the electric light, 

A second cause is, for instance, the fact that in each arc an E.M. 
F. is established opposite to the original E.M.F. and by no means 
to be neglected against it. This secondary E.iM.F. established in 
each arc appears to be a function of the current which passes the 
arc, most likely proportional to that current. Hence, if for a given 
current passing one arc this secondary E.M.F. be e, then the same 
current through n arcs, successively connected, would produce an 
E.M.F. equal to n e. This secondary E.M.F. n e is to be subtracted 
from the original E.M.F. ; and, internal resistance of the original 
E.M.F. plus resistance of leading wires having remained constant, 
we necessarily haA'e to decrease the total resistance of the n arcs 
in order to work with the same current as before. This merely 
means a decrease of the total length of the n arcs, or, which is the 
same, an increase of internal light or decrease of the measured or 
external light. A parallel connexion of the n arcs with reference 
to the poles of the given original E.M.F. would certainly produce 
only one secondary E.M.F. instead of n ; and for this reason it 
might be better to use the parallel circuit for the division of the 
electric light. But there are other very important objections to 
this solution. In the first place, as can be easily shown, the varia- 
tion of one arc has a far greater influence on the variation of the 
others in parallel, than in successive circuit. Further the length 
of each arc must be made very much smaller in parallel circuit 
than in consecutive cii'cuit. 

Another reason against an unlimited economical division of the 
electric light is constituted by the practical necessity that lamps, 
of whatever construction they may be, have a resistance inherent 
to their nature in addition to the resistance of the arc. For in- 
stance, in an ordinary lamp with an electromagnet, the resistance 
of the lamp consists of the resistance of the electromagnet plus the 
resistance of tlie two electrodes when metallically closed. This 
resistance, although small, is by no means nil, and cannot be neg- 
lected agauist the resistance of the arc, esi)ecially when strong 
currents are used. In other words, when producing the electric 
light in n points instead of one point, we are unable to practi- 

Intelligence and Miscellaneous Articles. 339 

cally fulfil the condition, that the sum of the resistances of the n 
arcs is equal to the resistance of one arc, to have the same current ; 
i. e. the former must be made smaller than the latter, on account 
of practical construction reasons. 

We may therefore sum up as follows : — The economical solution 
of the division of the electric light is theoreticcilhj quite possible, hut 
'practically difficult to obtain. The division can never become un- 
limited ; but ingenious inventors may nevertheless solve the problem 

The attempt by inventors to solve the question is therefore per- 
fectly legitimate. If their attempt cannot lead to a perfect solution, 
they may nevertheless do so approximately, and by it tend towards 
real progress in illumination, inasmuch as by their attempts the 
electric light may probably become more and more a successful 
general rival to gas, which at present the electric light certainly 
is not. 

Before I conclude, I must briefly avert to a paper on the Electric 
Light by Mr. W. H. Preece, published in the Philosophical Ma- 
gazine for January 1S79, in which the author believes that he 
has demonstrated from dynamical considerations that the di^dsion 
of the electric light is impossible. This it certainly is under the 
conditions introduced by Mr. Preece, ^iz. that the resistance of 
each voltaic arc, or each incandescent wire, is maintained constant. 
But it is unfair to the electric light to introduce this condition, 
especially as it does not at all represent the question at issue. 

When a number of lights are connected in series, the resistance 
of each must be diminished, and when a number of lights are joined 
parallel, the resistance of each must be increased in proportion to 
their number, so as to maintain the total external resistance con- 
stant. If !Mr. Preece ^nill introduce this condition into his equation, 
he will find that theoretically the division of the electric Kght is 
quite possible, i. e. that, theoretically, however the lights be ar- 
ranged, the unit of light -ttHl always be produced by the same 
expenditure of energ}'. Inventors should not, therefore, be down- 
hearted. On the other hand, investors in gas need not hasten to 
get rid of their shares ; for there are many questions invohdng 
practical difficulties which still remain to be solved ; but, at the 
same time, gas companies should be aware that they have a for- 
midable rival in the field, and bestir themselves to maintain the 
lead they hold by improving their owti means of illumination and 
extending its application. 


"\\Tien the interference-fringes produced by a biprism or Fresnel 
mirror are examined, the effect observed in "the focal plane of the 
eyepiece is the same as that which would result from two spherical 
waves emanating from the two images of the luminous source, and 
bounded respectively by the rectangular apertures occupying the place 

34U Intelligence and Miscellaneous Articles. 

of Ihe two mirrors or the two lialves of the prism. Fresnel {Memoires 
Mir la i/ijj'raclloii, \o\. i. ]). li."),") <'/^)r^^•^•^«/) assumes that, in the central 
part of the frinjj^es, the iliiiraction resulting; from this limitation of 
the w aves plays but an absolutely negligible part. On that hypo- 
thesis the fringes should all have the same breadth, proportional to 
the distance from the focal plane to the luminous images, the minima 
of intensity should all be nil, and all the maxima equal, in homoge- 
neous light, and in white light the central fringe should be of ab- 
solute whiteness. 

According to M. Weber *, attentive observation shows that these 
consequences are not exactly verified : the relative breadths of the 
lines vary with the distance of the sources from the focal plane in 
^\ hich they are observed ; the intensities of the maxima and minima 
differ very much ; in white light the central line is nearly always 
coloured. M. Weber arrives at the explanation of all these appear- 
ances by taking into account the fact that the waves which produce 
the phenomenon are not indetinite. By calculations necessarily 
long, and into the details of which we of course cannot enter, he 
first reduces the problem to the determination of IVesnel integrals, 
which he afterwards expresses by means of a Bessel function and 
another, analogous, definite integral. He thus obtains a compara- 
tively simple expression for the intensity of the light in any point 
of the interference-field. — BihlioOieque Unlverselle, Archives des 
Sciences physiques et naturelles, September 15, 1879, tome ii. 
pp. 360, 361. 


The air whose moisture is to be ascertained is introduced into a 
flask which is furnished with a thrice-perforated stopper. Through 
one of the perforations a glass tube is passed which reaches to the 
bottom, through the second a thermometer, and through the third 
a glass tube communicating, by means of an indian-rubber tube, 
with a manometer having oil for its liquid. Both the glass tubes 
can be closed by glass cocks. The indian-rubber tube is itself sur- 
rounded with a second one, filled with oil in order to prevent any 
diffusion of the aqueous vapour — a circumstance which Edelmanu 
(Wied. Ann. v. p. 455) has not taken into consideration. It might 
probably be advantageous to substitute glass for the Indian rubber. 
i''irst, a thiu-\Aalled glass sphere contaiuing anhydrous phosphoric 
acid is put into the flask, and is broken by shaking the latter, 
i'rom the variations of pressure in the manometer the amount of 
aqueous vapour is determined. In order that the previous volume 
of the air may be restored, the manometer consists of two glass 
tubes connected by one of indian rubber. The results were per- 
fectly satisfactory. — Beihldtter zu den Annalen der PhysiTc und 
CJiemie, 1879, No'. 9, p. 697. 

* Vierteljahrsschrift der Ziiricher naturforschenckn Gesellschaft, 1879. 








XL. On the Relation between the Thermoelectric Properties, 
the Specific Resistance, and the Hardness of Steel. By Carl 
Barus, Ph.D., of Cincinnati"^. 

[Plate XI. figs 1-6.J 

I. Introductory Remarks. 

THE experiments which gave rise to the follo\ving paper 
were commenced with the view of further studying the 
relation between the maximum of permanent magnetism, 
hardness, and form of steel, a subject proposed for inaugural 
work by Prof. Kohlrausch. 

Although this question had elicited considerable experimen- 
tation ever since Coulomb's time t, it was not until compara- 
tively recently that harmonious results were arrived at, chiefly 
through the labours of Ruths$, Rowland §, Gaugain||, Frommelf, 

* Communicated by the Author, having been read in extract before the 
Physico-Medical Society of Wiii-zburg on the 18th of January, 1879. 

t Coulomb, Biot. Phys. iii. p. 108, &c. ; Hansteen, Pogg. Ann. iii. 
p. 536, 1825 ; Miiller, Pogg. Ann, Ixxxv. p. 157, 1852 ; Pliicker, Pogg. 
Ann. xciv. p. 28, 1855; Wiedemann, Pogg. Ann. cvi. p. 169, 1859; 
Lamont, Handbuch d. Magnet, pp. 223, 249-253. 

X Inaugural Dissertation, p. 34 (Darmstadt, 1874) 

§ Phil. Mag. [4] 1. p. 361, 1875. 

II Comjit. liend. Ixxxii. p. 145, 1876. 

II Gott. Nachr. Nr. 7, 1876, p. 157 ci! seqq. 

Phil. May. S. 5. Vol. 8. No. 50. Nov. 1879. 2 A 

342 Dr. C. Barus on the Relation hetioeen the Thermoelectric 

Trovo and Durasssicr*, and Grayf. All these obsen'ers, 
however, have classified steel, with reference to its hardness, 
cither simply into hard and soft, or have accepted the colours 
of the oxide film of the tempered bar as a criterion of distinc- 
tion suflicient for their purposes. It seemed, therefore, that 
the most probable method of further elucidating the magnetic 
subject referred to would consist in attempting to find some 
method by which the hardness of steel can be more distinctly/ 
and more rationally expressed. My endeavour was, in other 
words, to give the very vague notion hardness as applied to 
steel a quantitative signification. So long, however, as the 
ultimate nature of hardness does not admit of accurate defini- 
tion, it is sufficient for the accomplishment of this end to exa- 
mine some of the other properties of steel which likewise vary 
with its hardness, and by considering the magnetic moment, 
ca'teris paribus, as dependent on the former, to eliminate, as 
it were, the notion of hardness between them. My attempt 
is, in short, to find an expression for the more complicated 
functions of hardness, cceteris imribus, in terms of the more 
simple. Of the latter the thermoelectric j^roperties and the sj-ie- 
cific resistance of steel, both admitting of accurate and easy de- 
termination, appear most suitable. 

As, however, the experiments on hardness and the elec- 
trical properties of steel alluded to, although only introduc- 
tory in their character, gave rise to a number of new results, 
I determined to publish them separately. To obtain as com- 
plete a picture as possible of these phenomena, I have made 
free use of all the information on the subject within my reach. 
In each case the author borrowed from is cited. 

II. Apparatus for Hardening Thin Steel Wire. 

For reasons which become apparent below |, the principal 
experiments of the following paper are confined to thin rods 
cut from the same coil. The rather difficult task of hardening 
these homogeneously throughout their length, without giving 
rise to a change in their chemical composition (either from 
oxidation or carburation), I believe I have accomplished by 
the aid of the following apparatus. 

A glass tube 200 to 300 millims. long, 8 millims. wide, was 
provided at a distance of about 80 millims. from one end with 
two opposite apertures a a (PI. XI. fig. 1), each about 3 millims. 
in diameter. This part was then surrounded by a cork A, 
perforated perpendicularly to the axis of the tube in a manner 

* Ann. (h Chim. et dc Phys. (5) v. p. 2GG, 1875. 
t Phil. Mag. [.5] vi. pp. 321-323, 1«78. 
t Difficulties due to structure, vulc vii., d. 

iLMag. S.5.Vol. 8. PI. XT. 





II . 


.. S. 






l/hnt<;t-nBro^ hAi^ 

HiiLMiig 5.S.Y6L 8 H XI. 

^^IT"^ / ^^'k/, \ 

fir'"' v!l'*^''\Zy » 


III ^ v^ v_^ 



Fi^ 4 F •( 


> ~i-^ 


1 r 

i • 

ft ^' 





J J 













' ' 


















■ y 

' w 







' -2^^<'^^ ^^ 


xT^ — 




























1 1 


















— r 




































Properties, Specific Resistance, and Hardness of Steel. 343 

to correspond with the holes a a. This arrangement is fas- 
tened vertically in a suitable iron stand (not shown in the 
figure). The Avire to be hardened is introduced into the tube 
and fastened below to a brass rod h h fitting tightly in the per- 
foration ha ah, and above to the spring d K. For the purpose 
of fastening the lower end, it was found sufficient, after having 
previously wound it round the rod h h so as to form a coil 
which could easily be made to slide off, to push the rod 
through ha ah and the coil, the latter having been introduced 
into the tube from the top. The spring d K, around the lower 
half of which the other end of the wire was wound, the upper 
half being provided with a clamp-screw g g, was fastened to a 
second arm of the stand (also omitted in the figure) . Bj pro- 
perly adjusting the rod h h and the arms of the stand, the wire 
could be brought into coincidence with the axis of the tube 
and stretched as far as was necessary. 

A powerful galvanic current heated the wire to the degree 
of redness desired. The former entered at gg and passed 
back to the battery through h h, as shown in the figure. To 
prevent the oxidation of the wire during the process of heat- 
ing, a current of dry CO2 gas * was passed through the tube, 
entering by means of the hose C attached to the lower end. 

After the wire had attained a steady uniform glow, the hose 
C was closed by the fingers, its connexion with the carbonic- 
acid apparatus disadjusted, the open end being connected with 
a neighbouring hydrant instead ; hereupon the faucet of the 
latter was quickly opened, the galvanic current being at the 
same time interrupted : the water dashing up the tube with 
great velocity, imparts to the wire the hardness desired. 
Before each experiment the parts of the apparatus were well 
dried in a warm current of air. 

The apparatus described presents the following advan- 
tages : — (1) By employing currents of different intensity, 
thus heating the wire to different degrees of redness, we are 
able to obtain corresponding degrees of hardness, which, 
though scarcely distinguishable mechanically (all appearing 
equally hard and brittle), have very different effects on the 
magnetic and electrical properties of steel f. (2) From the 

* Having accidentally employed moist carbonic-acid gas, a small flame 
was observed at the top of the tube. This is probably due to the com- 
bustion of both H^ and CO, the former being generated by the decomposi- 
tion of aqueous vapour by the hot steel, the latter by the action of the 
nascent II produced on the C02. 

t See IX. The coercive force of steel being a minimum at a point in 
incipient redness, it is possible that the apparatus might be used in ob- 
taining intense circularly or longitudinally magnetic wires. In the first 


344 Dr. C. Barus vn the Relation between the lliermoelectric 

fact that the wire is kept in a state of continual tension by the 
sjiring d K, and from the particular method of chilling, the 
wires remain straight after being hardened. (3) The very 
slight oxidation noticeable on the hard wires is probably due 
only to the contact of hot steel and water in the act of harden- 
ing. Disadvantages, however, arise from the fact that the use 
of the apparatus is confined to thin bars, and that the wires 
obtained may be in a condition of circular magnetization. 
This would partly prevent their employment in subsequent 
magnetic experiments. The difficulty may, however, be 
avoided by breaking the galvanic circuit a little before open- 
ing the faucet. 

III. Methods of Measuring the Hardness of Steel Electrically. 

(a) Thermoelectric Position and Hardness of Steel. 

In this place it wall be expedient to leave the special consi- 
deration of steel for a moment, turning our attention to the 
electromotive force of a thermoelement composed of any two 
dilforent metals A' and A". 

Kohlrausch has shown* that the phenomena included under 
the head of thermoelectricity can bo explained on the h}iio- 
thesis that the heat-current is always accoinpanied by an 
electric current whose intensity is proportional to the number 
of caloric units passing the same section. He thus arrives at 
an expression for the electromotive force between any two 
metals (A' and A"), which, if for simplicity we suppose the 
cold end to be kept at zero f, has the following form : 


where E^ is the electromotive force corresponding to a differ- 
ence of temperature t of the ends, (y — 3") a constant specific 
for the combination. , 

This expression of Kohlrausch is very convenient, inasmuch 
as it allows us to separate the actual electromotive force into 
two terms, of which the first, ^'t(J. +/(t)^, is dependent only 
on the metal A' and r, the second, •&'V(1+/t), only upon A" 
and T. 

Now wo know that the thermoelectric position of a metal is 

case the wires should be cooled without brcakinpr the current, in the 
second the tube surrounded by a coil through which, during: the act of 
bardenin<r, a powerful galvanic current flows. See Holtz, Wied. Ami. vii. 
p. 71, 1879. 

* Pogg. Ann. clvi. p. GOl, 1875. 

t The thermoelectromotive force being, according to Tait, Avenarius, 
Hankel, and others, a function of the temperatures of the two ends. 

Properties, Specific Resistance and Hardness of Steel. 345 

dependent not only on its chemical nature, but also on its me- 
chanical condition (hardness). Let us therefore put 

where ^'q and y„ are to represent the (absolute) constants de- 
pendent on the chemical nature of A' and A^' respectively, 6' 
and 6", however, varying with the hardness of the metals. 
Thus the above equation becomes 

E.= ](y,-n) + (^'-nJ<i+/(T)). 

But suppose that A' and A" are not different metals, but 
represent two rods to which different degrees of hardness have 
been imparted, which were originally, however, cut from the 
same wire. In this case (•&'o~'^''o)=^j whence 


dependent only oii t and the difference of hardness of the 

It wall be shown below that the electromotive force of an 
element of soft and hard steel varies continuously with the 
difference of temperatui'e r and with the difference of hard- 
ness of the rods. We will therefore put 6'' , the constant belong- 
ing to the soft bar {i. e. one which has been heated above red- 
ness and allowed to cool slowdy in a badly conducting medium), 
equal to zero, as it is in this that the molecules will most 
probably have assumed normal positions. If, furthermore, we 

E, = ^'t(1+/(t)) by E, = aT + Z.T2, 

a sufficient approximation for practice, we derive 
^i^=a + 25T and F^^l =a for t = 0. 

This expression, i. e. the limiting value of the electromotive 
force of a thermoelement composed of a soft rod and one of 
any degree of hardness to the corresponding difference of 
temperature * when the latter converges towards zero, wull in 
the following be taken as the measure of the hardness of the 
harder bar. I shall apply the term thermoelectric hardness to 
it throughout the following paper (abbreviated T. E. H.). 

The relation between the thermoelectric properties and 
hardness of steel, notwithstanding its comparative import- 
ance, has never, to my knowledge, been made the subject of 
detailed and exclusive study. All the experiments thus far 

* The colder end being supposed at 0". 

340 Dr. C. Barus on the Relation between the Thermoelectric 

published (the principal beintr those of Magnus*, Sir W. 
Tlionisonf, and E. Becquerol |) are of a qualitative nature, 
the results being derived from the direction of the current 
observed on bringing together, in one way or another, wires of 
different hardness. 

The experiments of Magnus being limited to hard-drawn 
wires, do not properly fall within the scope of the present 
paper. The same is true of a number of the exjieriments on 
steel in the excellent paper of Sir AV. Thomson. AVith regard 
to the effects of annealing, Prof. Thomson observes: — "In 
cases of round steel wire, of steel wire flattened through its 
whole length by hammering, and of steel watch-spring, the 
thermoelectric effects of annealing portions after the whole 
had been suddenly cooled was a current from unanncaled to 
annealed through hot." This result comprehends all that has 
thus far been done. 

(b) Specific Resistance and Hardness of Steel. 

With reference to the specific resistance and hardness of 
steel, \\Q shall proceed in a manner analogous to the preceding. 
Denoting the observed specific resistance of a bar by S, that 
part of S which is due only to the chemical nature of the rod 
by Soj that due to its hardness by ASq, we have 

S=So + ASo. 

Now, as it follows from results given below that the specific 
resistance of steel increases continuously with its hardness, it 
will be convenient to put ASq for a soft bar equal to zero. 
The value of AS^ for a bar of any degree of hardness thus 
numerically determined will in the following be accepted as 
a second measure of that property. 

The work thus far published on the relation between spe- 
cific resistance and hardness of steel is due principally to 
Mousson§. Of late results have also been announced by 
Chwolson II . The data of both observers agree only qualita- 
tively with mine. 

IV. Determination of Thermoelectric Hardness. Apparatus. 

Method. — In the determination of thermoelectric force the 
procedure known as Ohm's method was first employed. After- 

* Pogg. Ann. Ixxxiii. p. 486, 1851. 
t Phil. Trans, iii. pp. 7t)0-727, 1856. 
X Ann. de Chim. ct dt Phys. [4] viii. p. 402, 1866. 
§ K Denhschr. d. Seine, acsdlsch. [8] xiv. pp. 1-90, 1865. 
II Mel. I'hys. dc St. rcdrdvury, x. p. 370, 1877. Sw also Carl's Septet. 
xiv. p. 15, 1878. 

Properties, Specific Resistance, and Hardness of Steel. 347 

wards, however, it was found expedient to measure these 
forces (as Kohlrausch and Ammann * had done in similar 
experiments before) by a method of compensation, the object 
being to avoid the difficulties from the species of polarization 
duo to Peltier's phenomena. The method can be easily de- 
duced from that proposed by Bosscha, the latter, in the case 
where small electromotive forces are to be measured, admitting 
of simplification. 

In the diagram (fig. 4), E denotes the compensating element 
(1 Daniell element, =11*7 Weber-Siemens units), e the ther- 
moelectric couple whose electromotive force is to be deter- 
mined, both acting as shown in the figure, C a Weber's 
commutator (employed for reasons given below), G the gal- 
vanoscope. Let us represent the resistance of the branch a b 
by cf, that of the branch a E Z* by W + Jc, where W represents 
the large resistance of a rheostat interposed, k that of the re- 
mainder of the branch (about equal to 1 Siemens unit) inclu- 
ding E. 

When the current in G is zero, we have 
e .r 

E ^x+k+w 

But as the ratio =p is small, and therefore of necessity also a; 

(maximum value =10 Siemens units), in comparison with 
W + ^' + A' (about 20,000 Siemens units), we may with suffi- 
cient approximation put 

_ E 

the experimental accuracy obtainable allowing us to neglect 
k + X in comparison with W. In the experiments the branch 
a h was a small Siemens rheostat. 

The precise moment in which the current in the galvanoscope 
is equal to zero can be best determined by observing whether 
the needle on closing and opening the circuit remains at rest. 
This, however, is only possible when the opposed currents 
from e and E w^hich pass through the galvanoscope are closed 
simultaneously. To accomplish this, the little cups at the end 
of the rods 1 and 2 of the commutator were quite filled wdth 
mercury, those of 3 and 4 only partially. By this de^-ice, on 
closing, Ci and C2 are first brought into contact, and the cur- 
rent E CgCi^aWE, not passing through the galvanometer, 
comes into action ; in the next moment (C3 and C^ being 
joined) the current from e and the partial current from E re- 
ferred to are closed simultaneously. In this way also induc- 
* Pog-g. Ann. cxli. p. 459, 1870. 

348 Dr. C. Barus on the Relation between the Thermoelectnc 

tion-currents, which may possibly be generated in the rheostat, 
are without disturbinnr cffbct. The commutator merely serves 
the purpose of a double key. 

As the electromotive forces measured were all very small, 
the large resistance W could be left unaltered, so that 
e= const. A'. Now the resistance .r was so chosen that the 
intensity of the current from e exceeded that of the partial 
current from E by the minimum possible. The thermoelectric 
force, however, decreasing with the temperature (T — i = T) 
of the ends, a moment soon arrives at which the intensities of 
the two currents are equal, and the deflection of the needle =0 
in consequence. At this point the thermometers are read off. 
Tliermoelement. — Instead of measuring the electromotive 
force of soft and hard steel directly, it was found expedient to 
compare all the rods with one and the same piece of copper 
wire. By this means the apparatus could be considerably 
simplified and many practical difficulties avoided. The con- 
struction of the copper-steel couple is given in vertical section 
in fig. 2. 

To raise the ends of the steel rod to different temperatures, 
two doubly tubulated spherical receivers, each about 1 decim. 
in diameter, were used. These, held in position by movable 
supports of poorly conducting material, and so placed that the 
tubulures A and B were horizontal, the other two vertical, 
were connected by a glass rod c d fitting water-tight in the 
perforated corks adapted to the horizontal tubulures. This 
rod served a double purpose : by uniting the receivers as one, 
it prevented breakage of the very brittle steel rods, at the 
same time allowing them to be easily adjusted and removed; 
on the other hand, the receivers could by means of it be placed 
at any distjince apart, this being necessary, as the rods to be 
examined were of very different lengths. 

On one side of the glass rod the copper wires which acted 
as poles of the instrument Avere inserted once for all ; on 
the other tw^o appropriate holes served for the introduction 
of the steel rods s s to be tested. The ends of the latter were 
connected with the corresponding ends of the copper wires by 
small fiat clamp-screws of brass. 

The apparatus being thus ready for experiment, the two 
receivers were filled with distilled water at T and t degrees 
respectively^, whei-e t was so chosen as to differ but slightly 
from the temperature of the room. The thermometers (intro- 
duced through the vertical tubulures) Avere read off' Avith a 
telescope as follows : the deflection of the needle having 
become very small, t Avas determined, after Avhich, Avhen the 
current in G Avas =0, T, Avhereupon another check-reading 

Properties, Specific Resistance, and Hardness of Steel. 349 

of t was made. Before each observation, the water in the 
receivers was well stirred. 

Galvanoscope. — The galvanoscope used was a very delicate 
instrument of Sauerwald, provided with mirror and astatic 
needle. The deflection of the latter was read off by mirror 
and scale. As the telescope of this instrument stood side by 
side with the telescope of the thermometers, both readings 
could be conveniently made by the same observer. 

V. Determination of the Specific Resistance. 

For determining the specific resistance of steel rods, use 
was made of a Wheatstone-KirchhofTs bridge. An appro- 
priate mercury commutator allowed the observer to inter- 
change the unknown resistances without altering the value 
of those belonging to the bridge proper. Thermoelectric dis- 
turbances were avoided as far as possible by closing the cur- 
rent (one Smee with large resistance) only for very short 
intervals of time. Finally they were eliminated completely 
by replacing the hydroelectromotive force by a Weber's 
magneto-inductor *. The resistances of all rods were deter- 
mined in terms of an arbitrary standard S (0'0312 Siemens 
unit at 0°), chosen to correspond in magnitude with the un- 
known resistances. The galvanometer used was the one already 
mentioned above. 

As the resistances to be measured were all very small 
(0*1 to O'Ol Siemens unit), great care had to be taken to 
exclude all disturbing resistances arising from insufficient 
contact. Soldering could not be resorted to, as it was believed 
that the ends would thereby have been annealed. The method 
adopted was as follows : — The ends of the rods having been 
well cleansed, were covered to about 1 centim. with a thin 
adhesive film of galvanically deposited copper, which was 
thereupon amalgamated (easily accomplished by plunging the 
freshly covered part in mercury). The rod thus prepared was 
then fixed, together Avith a glass rod in two corks, in a manner 
similar to that employed in the case of the thermoelement, 
and the whole, except the amalgamated ends, covered with a 
thick coat of varnish. Suitable wooden cups provided with 
horizontal and vertical apertures completed the connexion of 

* Pogg. A)m. cxlii. p. 418, 1871. The use of the magneto-inductor in 
connexion with the bridge was suggested bj Kohkauschr This physicist 
also showed that this method is applicable even when the resistances to 
be determined are in the form of coils, the extra cun-ents produced being 
calculable. I found the application of great convenience, inasmuch as the 
observer always has the needle of a delicate galvanometer completely 
under his control. 

350 Dr. C. Barus on the Relation between the Thermoelectric 

the rods with their respective parts of the bridge by means of 

The efficient length was determined by deducting from 
the total length that of the amalgamated ends. For the mea- 
surement of the diameter, use was made of the microscope ; 
a determination of this dimension from known length, weight, 
and specific gravity was impracticiible, inasmuch as the use of 
the pycnometer, which alone would have given sufficiently 
accurate results, would have compelled mo to break the rods. 

VI. Experimental Results. 

A. Thermoelectric Hardness of Rods suddenly immersed in 
Cold Wuter ichile in different states of Red Heat. 

The following (older) results were obtained directly by 
Ohm's method. E^ was put = const, t — a condition nearly 
fulfilled by couples of soft and hard steel between 0° and 80°, 
in which case also the T. E. H. and the constant of propor- 
tionality are identical. The rods were hardened in the appa- 
ratus described in § II. ; diameter =0'678 millim. ; the num- 
bers preceded by the point (•) were afterwards checked by 
the method of compensation. T. E. H. is expressed in Weber- 
Siemens units. 

The third column of the following Table contains the num- 
ber of large Bunsen cells employed in the heating of the wire, 
the fourth the observed degree of redness at the time of sudden 

Table I. 


T. E. H. 





Soft, cooled slowly. 




Below redness. 











• Dark red. 






I 9 







1 11 



I 12 



. Brick-red. 

■! 14 









Properties, Specijic Resistance, and Hardness of Steel. 351 

The Bunsen cups were introduced without altering the re- 
maining parts of the circuit. The length of the wire heated 
was not in all cases the same. 

B. The following determinations were made in the summer 
of 1878 ; temperature of the room very constant, and at about 
20°, this, as already observed, being nearly the same as t, the 
temperature of the water in the colder receiver. The method 
of compensation was employed throughout. The determina- 
tion of T was effected by a Geissler normal thermometer (gra- 
duated in 0°"1), that of i by an ordinary instrument (graduated 
in 0°"2), which had, however, been carefully compared with 
the former. 

In Tables II. and III. the difference of temperature of the 
ends of the steel rod is given under r, the corresponding elec- 
tromotive force for the elements copper-steel under JE,. ; a and 
/3 are constants which satisfy the equation Ej=aT—^T^. 
These were calculated by first computing their proximate 
values out of two distant observations, and then adding to 
them corrections deduced from five of the most satisfactory 
observations by the method of least squares. 

If, now, we denote by a and b the constants for an ele- 
ment of soft steel, hard steel corresponding to those a, /3 and 
a', /3' of the same rods when compared with copper, we shall 
have, since E^=aT—^T^ and E'^=(Jt—^'t^, 

But Er—Ej=^T, the electromotive force of the element 
steel-steel; so that, since also E^=aT— 6t^, 

a = a. — a'. 

The constants a and b are given in the last two columns. 
a may be regarded as numerically equal to the T. E. H. above 
defined, as E^ is nearly a Knear function of r. 

352 Dr. C. Barus on the Relation between the Thermoelectric 




o " 





09 O 


c o = . 










•s =" 


J2 2 

'3 -TO 



1 o o 


■1- vi 












































































































^ A 

^^ * ^ 

^ * -V 

, » ^ 


t- ?0 O CI o 

l^ C 01 C5 o 

ir: crxr-^o 

^ CO VC — o 


in CO 00 i: CO 

o o t- -r lo 

c; oi ^ :;■ -H 

X >0 C t r< 

TJH O C5 X o 

X — iC CO Cl 

C uo Ol t^ X 

X O -< >-0 o 


^ oj CO ■* o 

t-H 00 tMt: o 

—1 —. S^l I^^ (M 

w r-l OI (M OI 













-+ 1^ -H O r-l 

'* I? !r y "^ 

01 01 :o Ol O 

X -r X C: lO 


cr CO ix «.- CO 

^-71/ 1 * --H 

t^ lO C: t^ rt 


-r o o X o 

X — ^ i'^ r* ~~^ 

—1 1- r'l 1- x 

X C^ <— lO o 

r>^ ^ 

•— 1 O) CO -* o 

-^ c-:) -i^ ir. L-. 

-H ^ oi 01 01 

o -H OI oi OI 











01 X X Tt; o 

c c: X CO oi 

O CO O uO t- 

>.o c ~ c m 
01 oi .p C-. CO 

t-. CO :r oi ■* 

O C: t-co 'f 


r: ih r: r: oj 

t- ^ i^ i CO 

rt CO '^ IS :c 

ci oi ^ ~o — 


^- , ' 

^ ' 

V , 

, ' 




1— 1 


Properties, Specific Resistance, and Hardness of Seeel. 353 





•^ >;>= 

o 5 "^ 


ii a %. 









"3 " 2 



o c3 

S S3 


o t 



^ S 

^ ?3 



^ -S 

tie tn . 

E i 

'S g 

"o ^ 

iiT3 O 




g 2 S 

d - 

c - 

6 - 

































C5 O 





o o 


o o 



8 o 



o o 













• 8 


































^. • ^ 




O CO lO (X) CO 

-H G0^~^^^o 

CO Ol -rl rH CO 

O-H Or— t- 

O CO O T-i c-i 

lO CD iC' t- 'tl 

l- CO I- CC CI 

l^ C'l CO "-1 IM 

O O -f CO o 

O r-f ,-lrt (H 

OrH,-l(M (M 

O r-( ,-( 1-1 1-1 








■-H oo-*co»o 

■* -rt< -t< Tt< (M 

O -t< lO ^ CO 

CD 00 t- O (M 

■* lO CD I- CO 

t^ CO t- 00 C3 

I- Ol OC -H Ol 

CD O ^ COCi 

O -H r-l r-H C-^ 

o r-(,-( (^^l^^ 








O •* 1-H O iM 

-ti 00 -HOO 

IM »0 O O O 

t-'ODO 0-* 


Tt< ^H P r-H TtH 

ib-^eb >b C5 


CO r-H IC OTlb 

^ ?o ^ ^m 

1—1 CO O CD CO 

^ CO-* CDO 

V. ^ ■ 

■ ,, ' 

^ — - 



1— J 



1— 1 

1— 1 

1— 1 






354 Dr. C. Barus on the Relation between the Thermoelectric 






S _ 










" , 






















































































■ § 































' 1 

^, « — ^ 


-* -^ 

1 -^ 


X ■?! rj cj irt 

X t- :r X ^ 

2:u:i3?^ g 

^ ^ Cl Cl CO 


Cl — X t- ^ 

Cl i-O f -r o 

S c — a: 5 

tc in O =C X 

S '^ ^ '■" "''* 

'^ coiC Ci C5 

c^ -^ ■^ ■^ ^ 

2 Cl CI CO CO 

Cl ci CO CO CO 










OC' C: t^ C: 00 
Cvl »?< u- it ^ 

~ X CO r; ;r 

r^ o o o C~- 

'^'z!'* £r i3 


CO --1 1-- X o 

c; 5" "^ CO X 

C5 o o -^r o 

I— 1 lO -1- CO C5 


C5 :3 ^ X n 

-J m I.- ->:: X 

g cocr ascj 

£1 rt< Tj<Tr Tf 

— • Cl Cl CO CO 

— i Cl CO 00 CO 







X i.": X -t -r 

c: X t- — >-: 

?r C uo 01 t;- 

Cl L- X i." CI 

CO c^ c; c: X 

-f C: -t 9 CI 

X CU^ — • CO 


CI ih tb 'h :j^ 

i ^ Cl j~ C5 

CI ^t i -- Cl 

6 t-co X o 

c? -*■ -r iH i-~ 

01 CO CO -+ ^ 

CO CO o :c :c 

.-1 Cl ■* i-0 o 

^ J 

V , ' 

j " , 

V , ' 












Properties, Specijlc Resistance, aud Hardness of Steel. 355 

The following Tables IV. and V. contain the specific resist- 
ances of the rods already cited in Tables II. and III. The 
data are given in terms of mercury. The column S contains 
the total specific resistances, ASq the corresponding excess of 

the latter over that of the normal rod I. Of the ratio rp ti "ir 

mention will be made hereafter. " ' ' 

Let lis denote by a and h the resistances of the two parts of 
the first branch of the bridge on each side of the sliding con- 
tact, by K' and K''' the resistances of the corresponding parts 
(thick copper wire) of the second branch, into which the un- 
known resistances W and R are inserted ; finally, by S the 
standard of comparison above referred to, in terms of which 
W and R are to be determined. When the current in the 
galvanometer is zero, we shall have for a particular position 
of the commutator, if we introduce 

(1) W and R alone 

(2) W and R with h on the right, 

a' W + K' 

V R + K'' + S' 
(3) W and R with 8 on the left, 

h"~ R + K'' 

Three similar equations may also be derived for the other 
position of the commutator, as only W and R are interchanged. 
From these six equations we deduce: — 

First position. 

Second position. 

R K^ 

W K;; 

8 "^ s 

R K' 

8 "^ 8 

a" __ a 

W h 

a a 


356 Dr. C. Barus on the Relation between the Thermoelectric 

-Y «^nd -^ were determined in the same way previous to 

the experiments, and their values checked from time to time. 
In coniparintT the resistances I. . . . IX. and A . . . D, the tol- 
lowing plan was observed : — 




.... VIII 



And in the same way 
1 with A . . . D. 

R:(5 ... 







Each of the data is therefore derived as a mean of four deter- 
minations. Possible heterogeneity of the wire a + 6 thus 
becomes less effective. 

As an example, I will add results obtained for the rod C 
(resist. =0-0051 Siem. U.):— 










Ist position 

W : 5 = 




2ud position 

W: 5 = 








For the rod I (resist. = 0'0542 S. U.) on different occasions, 
1*735 and 1*741 were found for "W : S. 

As will be seen, the principle stress was put on the relative 
values of the resistances. To facilitate orientation, however, 
the results were approximately reduced to Siem. units by de- 
termining the standard S in that denomination. 

Assuming the coefficient for temperature for steel to be the 
same as that for copper, the results obtained will be good for 
0° C. directly, S having been previously reduced. Although 
this is only approximately true, the influence of this difficulty 
on the relative values of the resistances will be but slight, as 
the temperature of the room remained nearly constant. 

Table IV. 






T. E. II. 











«I\V ... 






























1 The resistances marked with au asterisk were determined by using 
the magueto-iuductor as cuiTont-oeDerator. lu the others a Smee element 
was employed. 

Properties, Specific Resistance, and Hardness of Sttel. 357 
Table V. 





T. E. H." 




0005] 2 




The experiments now following, under the heads C and D, 
have more a descriptive character than one of precise measure- 
ment; the results are therefore given with one decimal less. 
For the determination of T. E. H. the rods coming under 
these heads were compared indirectly with the rod VIII. 
(Table II.), for the T. E. H. of which the number 0-000069 
(as above found) was assumed. 

_C. The T. E. H. and ASo for glass-hard rods; diameter =2-30 
millims. These were hardened by the aid of a blast-lamp. 
The flame of the latter was for this purpose directed horizon- 
tally and placed directly over a trough containing cold water. 
In this way the rod could be transferred with great rapidity 
out of the flame into the water. 

Table VI. 


T. E. H. 




T. E. H." 







2100 1 

Heated yellow and sud- 
denly cooled. 


1311 — 




1) II I) 


130| — 




I) 11 i> 


130 00129 





116 107 



2000 j 

Heated red and suddenly 

Obtained by reheating 







[III] and [IV] to yel- 





lowness and suddenly 

D. The T. E. H. and ASq of rods 0-678 in diameter, har- 
dened t in the apparatus § II., afterwards annealed by immer- 
sion in hot linseed-oil. 

t The T. E. H. of these rods in the glass-hard condition varied from 
50 : 10« to GO : 10«. 

Fhil. Mag, S. 5, Vol. 8. No. 50. Nov. 1879. 


358 Dr. C. Barus on tlie Relation between the Thermoelectric 

Table VII. 


T. E. H. 




T. E. H. 


# 1. 

# 2. 
» 3. 
» 4. 
« 5. 

* 6, 
» 7. 
» 8. 

* 9. 





2100 ^ 




2500 ; 



2100 \ 





Aunealetl at 300° t. 

Annealed at 280°. 

Annealed at 240°. 

Annealed at 200°. 
Annealed at 150°. 

£!!S \ -0000004 0-(>420 
iron. J 



f Heated in flame of a Bun- 
— -1 sen burner to redness and 
[ allowed to cool in air. 

E. The resistances thus far determined being so very small, 
it -was to be feared that, in spite of the continuity apparent in 
their variation, errors from insufficient contact might have 
conspired in producing illusory results. For these reasons 
check-experiments with longer wires were made, the resistance 
of some of which (I. to V.) is sufficiently great to admit of 
direct comparison with the Siemens unit (etalon). To ensure 
a more homogeneous hardening, these wires were spirally 
wrapt around a round stick of wood, and the length and dia- 
meter of the coils resulting so determined that the whole 
during the process of heating could be brought within the 
mantle of the blast-flame. In other respects the method given 
under C was pursued. 

Table VIII. 



Length. ^J''^- 
° meter. 











Heated yellow and immersed. 







>I M >I 













„ br. red „ ,, 







„ br. yellow,, „ 







,, br, red „ „ [darker. 







Heated br. red and immersed ; ends 







„ ,, 

t Rods 1 to 5 remained in tlie bntli during tbe whole process; the 

Properties, Specific Resistance, and Hardness of Steel. 359 

Spirals II. and IV. were afterwards softened by beating to 
redness in a Bunsen burner. Their specific resistance in this 
condition was found to be (without allowing for the smaller 

*IL So=0-154, *IV. So=0-159. 

Finally, in order to compare the results determined with 
induction-currents with those in which a Smee was employed, 
certain of the experiments were repeated. The agreement 
was entirely satisfactory. 

Deductions and Supplementary Experiments. 
YII. Hardness and Thermoelectric Properties of Steel. 

a. From the data contained in Tables II., III., and VII. 
we derive that the thermoelectric position of steel progresses 
continuously tcith its degree of hardness, or, in other words, 
thermoelectric and mechanical hardness are direct functions 
one of another. 

This statement involves the assumption that a rod cannot 
pass from the glass-hard (maximum) to the soft state (mini- 
mum) without passing through every intermediate stage — or 
that, by proper methods of annealing, every state between the 
maximum and minimum could be produced. This, I dare say, 
will generally be admitted. 

As of further interest I may add : — (1) that rods cut from 
the same wire and glasshardened in the same way possess also 
the same thermoelectric hardness (Table VI.); (2) this is the 
case even when the rods are carefully rehardened (rods [III]', 
[V]', Table VI.); (3) that if we start from like maxima, the 
thermo-current ahcai/s jyasses from the less to the more annealed 
through tcarm, (The direction of the current was independently 

h. From an examination of the data obtained from different 
material, we infer that the T. E. H. of soft and similarly an- 
nealed rods approximates to the same value*; that the value of 

others were immersed but for two or three minutes. The temperature at 
which the rods 6 and 7 were annealed could not be determined with cer- 
tainty, a microscopic air-bubble in the neck of the mercury-reservoir 
ha^dng given rise to a rupture of the thread. 

* In order to compare the degree of hardness con-esponding to a parti- 
cular oxide tint with that corresponding to a particular temperature of 
the oil-bath, use was made of the Tables to be found in Frick's Physikal. 
Technik, 3 ed. p. 377; also Wagner, Chem. Tech. 8 ed. p. 29. On the 
authority of these, 230° corresponds to yellow-, 290° to blue-annealed. 
We should therefore expect rods 6, 7, and 8, 9 (Table YII.) to agree with 
rods C and B (Table III.), respectively. This is sulEciently the case. 


3G0 Dr. 0. Bams on the Relation heticcen the Thermoelectric 

this coiisfmit for glass-hard rods is remarhahly different. The 
rods in Table VL, for instiince, possess a T. E. H. amounting 
nearly to 140 : 10"; whereas in the rods in Table II. the maxi- 
nuun* value found does not exceed 70: 10". This may be 
due to a dilt'erence in thickness, or, more probably, to a dif- 
ference in the composition of the rods examined. 

These ])henomena were further studied through the follow- 
ing ex})eriments. 

1. Commercial rods of different diameters were glasshard- 
ened and examined Avith reference to the current jiroduced 
when one end of a couple was cooled with a wedg('-slia})cd 
piece of ice. In general, a maximum of T. E. H. was ob- 
served in rods whose diameters lay between 1 and 2 millims. 
These experiments, however, are unsatisfactory, inasmuch as 
the composition of the rods enters as an element of disturb- 
ance which cannot be allowed for. For this reason experi- 
ments were made on thick bars, the parts of which had been 
filed to different diameters. 

2. The halves of each of two pieces cut from the same 
rod 5 millims. in diameter were reduced t by filing to thick- 
nesses of 3 and 1 millim. respectively, and glasshardened. 
During the process of heating, care was taken to raise all parts 
of the bars to the same degree of redness. On connecting 
the ends with the galvanometer and applying the ice wedge 
at the middle (where the diameter enlarged), very decided 
currents were observed passing from thin to thick through 
warm. Hereupon two cones were filed from the same mate- 
rial (5 millims. base and 50 millims. long). Point and base 
of the cones (previously glasshardened) being connected with 
the galvanoscope, the ice wedge applied at any point pro- 
duced in each case currents from apex to base through warm, 
thus harmonizing with the previous experiments. Near the 
points only the results became uncertain. On bringing toge- 
ther the cones with the rod [IV] (Table VI.), the points were 
found thermoelectrically harder, the bases softer, tlian the 
former. On the other hand, the point of a fine needle pre- 
pared from the same material gave contrary indications ; the 
line point therefore was apparently softer than rod [IV]. 

3. Finally, tA\o very gradually tapering cones were pre- 
pared from another steel rod 2"8 millims. in diameter. Con- 

• These rods (Table II,), even when heated to the utmost white and 
suddenly cooled, remainod strongly electropositive towards copper. 
T. E. II. therefore even in this extreme case -was much less than 107 : 10«. 

t It is to be observed that the thinner parts of these pieces sooner 
arrive at red heat and remain longer in this condition than the thicker 
parts. This applies equally to the cones. 

Properties, Specific Resistance, and Hardness of Steel. 361 

nexions with the galvanometer being made, the application 
of the ice wedge to the parts near the base generated a current 
from thin to thick through warm, to parts near the apex a 
current in the opposite direction; finally, between these a 
position was found at which the application of the ice wedge 
produced no current at all. This occurred at parts about 
i-5 millim. in diameter. The other cone gave like results. 

4. When the bases of two similar cones of the same mate- 
rial are connected with the galvanometer and their apices 
brought into contact, upon warming the latter, a current in one 
direction or another will be produced — this from the fact that 
the points are rarely equally hard. Experiment shows, how- 
ever, that by consecutively warming parts which lie symmetri- 
cally to the right and left of the apices in contact, currents in 
opposite directions are the effect. Herefrom it follows that 
these currents originate each in a single cone. 

In endeavouring to generalize from these experiments, 
attention must be paid to the following points : — a. The 
maximum value of T. E. H. attainable is dependent on the 
quantity of carbon contained in the steel. The thermoelec- 
tric difference between rods of soft and suddenly cooled 
wrought iron can, for instance, be neglected in comparison 
with the corresponding difference of soft and hard steel. 
b. T. E. H. is influenced by the temperature of the rod when 
suddenly chilled (VII. c) as well as by the time of heating, 
the latter affecting the composition, c. By the form of the 
piece of steel and the method of sudden cooling, the internal 
structure of the mass being thereby modified (VII. d). 
d. Finally, we might add that in the time elapsing between 
the removal of the rod out of the fire and the subsequent im- 
mersion, the loss of heat by radiation will be relatively greater 
in the case of thin than in the case of thick rods. 

With these facts in mind, we may conclude that the maxi- 
mum values of T. E. H. attainable by glass-hardening rods of 
the same composition increases as the thickness diminishes ; 
that as this dimension continues to decrease a diameter is 
reached at which the negative effects of decarbonization are 
equal to and finally overcome the positive effects due to dimi- 
nution of diameter. 

c. From the results contained in Table I. there follows : 
the hardness of steel does not increase continuously icith its tem- 
perature at the moment of sudden cooling, hut at a point 
lying in dark-red heat the glass-hard state is suddenly attained. 
From this point on, however, the degree of glasshardness 
(measured thermoelectrically) continues to increase with the 
temperature. This observation conduces to the conclusion 

3G2 Dr. C. Barus on the Relation between the Thermoelectric 

that the change of state due to elasshardening is chemical in 
its nature. In this opinion I believe most chemists at pre- 
sent also concur, it being assumed that the uncombined carbon 
in soft steel is, by sudden immersion, converted into the che- 
mically combined. In summing up the facts by which the 
h}'pothesis is furthermore supported, we will mention, in the 
first place, the detailed analogy* which exists between the 
white pig used in the manufacture of Bessemer steel and glass- 
hard steel, on the one hand, and ordinary (grey) cast iron and 
soft steel on the other, the former containing carbon only in 
the combined, the latter also in considerable proportion in the 
uncombined state. Secondly, hardening by a process of wire- 
pulling, hammering, &c., will in all probability increase the 
specific gravity of steel ; hardening by sudden cooling, as is 
well known, diminishes it. In the former case, the thermo- 
electric current usually passes from soft to hard through 
warmf; in the latter, in a contrary direction. Indrawn wire 
the specific resistance is smaller| in hard-tempered, and greater 
than that of the same wire in the soft state. 

Considering these facts as a whole, we are perhaps justified 
in distinguishing between a process of chonical and a process 
of mechanical hardening. This, however, does not prevent us 
from paying due regard to the series of physical phenomena 
which always accompany the former. To these the peculiar 
internal structure of glass-hard bars, the warping which fre- 
quently attends sudden cooling &c., are to be referred. Vse 
conclude, therefore, that the cause chiefly influential in bringing 
about glasshardness in steel is chemical in its nature, and that 
in consequence of the physical phenomena wliich invariably 
accompany it the degree of glasshardness is more or less mo- 
dified. On the latter ground the continual increase of the 
T. E. H. after the critical temperature above referred to has 
been reached is to be explained. 

cl. The observed T. E. H. can of course only be assumed as 
directly expressive of its hardness when the rod umler experi- 
mentation is homogeneous throughout. This is approximately 
the case for thin rods. In thick bars which in the glass-hard 
state may be considered as made up of a series of concentric 
cylindrical shells, the hardness of which decreases rapidly as 

* See Wagner's Chcm. Techno!. 8 ed. ^p. 14, 15, 29. These analogies 
refer to mechanical properties, method ol preparation, colour. 

t Magnus, Togg. Ami. Ixxxiii. p. 460, 1851 ; Sir W. Thomson, Phil. 
Ti-ans. iii. p. 722, 185(5. 

X Mousson, X. Dcnksc/ir. der sdnceiz. Gesellsch. xiv. 8. pp. 1-90. The 
reader is also referred to Chwolson, Carls. Rcpert. xiv. p. lo. 

Properties, Specific Resistance, and Hardness of Steel. 363 

we pass from the exterior to the interior, the circumstances 
become more complicated. 

Furthermore, suppose the ends of a thick glass-hard cylinder 
to be kept at temperatures T and t (T > t). In this case, 
since each of the infinitesimally thin cylindrical shells has a 
particular T. E. H. corresponding to its hardness, we are led 
to infer that thermo-currents closing themselves in the inte- 
rior of the cylinder are the result — the direction of these in 
the outer (harder) parts being from t to T, in the inner from T 
to t. In fig. 3 (vertical section) the hypothetical condition of 
the cylinder in this case is indicated. As will be seen, its elec- 
trical state corresponds with that of a rod circularly magnetized. 

For the purpose of studying this question experimentally, 
a steel cylinder, 30 millims. in diameter and 50 millims. long, 
was turned and glasshardened. This was placed vertically 
directly before the needle of a magnetometer (the deflection 
of which could be read off with telescope and scale) in such a 
manner that the position of equilibrium of the needle was left 
unaltered. The relative position of needle and cylinder, in 
other words, was such that the axis of the former, if prolonged, 
Avould intersect the axis of the latter at its middle point. 
Upon now cooling the upper end of the cylinder with a piece 
of ice, or warming by projecting a jet of steam against it, very 
decided deflections were observed toward the right or left re- 
spectively, which increased with the difference of temperature 
T — ^, and vanished as this difference became nil. 

As the cylinder was not magnetic, it is improbable that these 
phenomena can be referred to a change in the state of mag- 
netic distribution. "With reference to the direction of the 
currents, however, no simple results could be arrived at. 

e. In § VII. c, we ascribed the very high value of the 
T. E. H. of a glass-hard steel rod to the large proportion of 
chemically combined carbon contained therein. If this be 
true, the thermoelectric difference between soft steel and soft 
iron, in both of which combined carbon is either wholly absent 
or exists only in traces, must be quite small. This inference 
is supported by the data actually found for soft iron. Making 
allowance for the difference of circumstances involved, the 
result to be derived from experiments of Kohlrausch and 
Ammaun also agrees sufficiently herewith. 

On the other hand, Joule * has Ion o- since shown that ordi- 
nary cast iron is thermoelectrically negative towards copper, 
all the more, therefore, towards soft steel — a result which we 
should be inclined to predict from the quantity of combined 
carbon contained. 

* Joule, Phil. Mag. [4], vol. xv. pp. o;j8, 539, 1857. 

3()4 Dr. C. Barus on the Relation between the Thermoelectric 

The minimum values o/T. E. H. (obtained by cooling tlie 
red-hot bar as slowly as possible) of different kinds of steel* 
and of soft iron are therefore approximately the sa?ne ; whereas 
the ma.vimum value of this constant (obtained by cooling the 
highly heated bar as rapidly as possible) differ enormously, 
this diff'erence being a direct function of the quantity of carbon 

f. Sir W. Thomson t has shown that in a thermoelement 
consisting of magnetized and nnniagnetized steel of the same 
hardness and form, thernio-currents due only to magnetic 
diff'erence can be generated. The direction of these currents 
was found to be in one case from unmagnetized to longitudi- 
nally magnetized through warm, in another from transversely 
magnetized to unmagnetized through warm, therefore also 
from transversely to longitudinally magnetized through warm. 

For the purpose of informing myself of the magnitude of 
the thermo-diiierence thus produced, the following exjieriment 
was made: — A soft rod (I., Table II.) was tested for its 
electromotive force when combined with copper (as described 
above, p. 348), and the locus of the equation Ei. = aT — /Sr- con- 
structed from fifteen very carefully made observations. 

Hereupon a large magnetic battery weighing 40 lbs. was so 
placed that each of the ends of the horseshoe touched a re- 
ceiver. The distance between the poles of the magnet and 
the corresponding ends of the steel rod was thus about 5 
centims. A second series of fifteen observations was now 
made. Upon comparing the locus of the latter with that of 
the former, the two curves coincided so completely that no 
influence could be discerned. Herefrom Ave conclude that 
the thermoelectric efiect due to a difference of magnetic state 
may, in comparison with those which can be produced by a 
difference in hardness, he comp)letely neglected. 

g. A very curious analogy was found in comparing the re- 
sults at which Frommet arrived, in studying the specif c gra- 
vity of differently tempered steel, with the T. E. H. of similar 
rods as found in my experiments. Dr. Fromme, if I infer 
correctly, limited his experiments to rods Avhose diameter was 
greater "than 2 millims. and less than 7 millims. His results 
are contained in the following Table, the volume of the soft 
bar being put = unity. 

* Steel is here used a.s distinguished from iron only by containing a 
greater proportion of carbon. iSo attention has been paid in this paper to 
the eflects of P, S, Si, Mn, kc, so often present in both. 

t Phil. Trans, iii. pp. 722-7i*7, 1856. 

I Fromme, doli'DHj. Xg'/u: 1<>3, 1870. 

Properties, Specific Resistance, and Hardness of Steel. 365 
Table IX. 



Increase of 

T. E. H. 

Soft .; 





" Yellow " 

" GrIuss-liarcV 

In the fourth column the T. E. H. of rods cited in Table III. 
(these, as I believe, corresponding very nearly to those for 
which the data of Fromme apply) is added. If we take into 
consideration that the results were obtained from different 
material, the parallelism observable is striking. To the very 
large difference between glass-hard and yellow-annealed 
when compared Avith the much smaller difference between 
yellow and blue, blue and soft, as seen in both observations, I 
would once more call attention. The fact that glass-hard rods 
can be considerably annealed at comparatively low tempera- 
tures, must be regarded as an adequate indication of their un- 
natural strained condition. 

A second result of Fromme, that the speciiic gravity of thin 
rods suffers greater loss by glasshardening than that of thick 
rods, also harmonizes with the conclusions drawn in § YII. h 
with reference to the T. E. H. of such bars. 

VIII. Hardness and Specific Resistance of Steel. 

From the data found for specific resistance of steel rods 
of different hardness, inferences analogous to the above may 
be deduced : — 

a. The specific resistance of steel increases continuously icith 
its mechanical hardness. 

b. Rods like-annealed differ but slightly, glass-hard rods 
considerably with respect to their specific resistance. 

c. On comparing the values found for the ratio > J~Q 

T. E. H' 

we infer that the specific resistance of steel is approximately 'a 
linear function of its thernwelctric hardness. In fig. 5 these 
results ai'e graphically represented. 

I will remark, howevei-, that the assumption of propor- 
tionality as based on the above figures is to be regarded as a 
first approximation only, notwithstanding the fact that the 
discrepancies fall within the errors of experiment. A rio-id 
discussion of the latter comes more appropriately within the 
scope of another paper, soon to appear. In thi.- place I would 

3()G Dr. C. Barus on the Relation between the Thermoelectric 

only call attention to the following. In the thick bars expe- 

rimented upon the value of ^ t^ u is usually too large — a fact 

which is easily accounted for, as the unavoidable resistances 
of contact above referred to will in this case have a relatively 
great effect, the resistance of the bars themselves being very 
small. In the rods included in Table VI. it was impossible to 
secure a uniform redness throughout, the ends invariably re- 
maining darker. As, however, T. E. H. depends princij)ally 
on the warm end, and AS^ on the mean hardness of the 
whole bar, we have thus a second cause for an overlarge ratio. 
So much, however, I think I have fully established, that 
T. E. H. and specific resistance of steel throughout their varia- 
tion are very simple functions one of another. T. E. H. and 
specific resistance must therefore be looked upon as effects of 
the same cause, as phenomena having some very intimate 

d. Particular attention must here be called to the remark- 
able result that the specific resistance of steel can by a pro- 
cess of glasshardening be increased to nearly three times its 
value in soft steel *. As this datum far exceeds that deter- 
mined by Mousson (about 25 per cent.), it is not without some 
hesitation that I make it public. The care bestowed on the 
experiments, however, together with the regularity observable 
in the variation of the results, I believe, sufficiently ensure 
their correctness. See moreover § VI., Ef. 

e. As deserving special notice, I will further add that the 
thermo-current always passes from the bar Avith greater to the 
bar with less specific resistance. The few exceptions to this 
fact in the Tables were afterwards found to be referable to 
errors of experiment by direct observation t. 

* It is to be observed, however, tli.attlie difierence between tlie specific 
resistance of steel in the soft and hard states is dependent on the compo- 
sition, increasing with the quantity of carbon contained from a very small 
value in soft iron to the -\ery large value above announced for steel. 

t Chwolson reports the increase of resistance due to glasshardening to 
be only OG per cent. This I can only explain by supposing the results 
of this observer to have been obtained from wires suddenly cooled at a 
temperature below that referred to in "S'll., c. 

X I would here again refer to the fact that, according to jNIagnus, 
Thomson, and Mousson, drawn steel wire and hard-tempered steel are 
ou different sides of soft steel, both with respect to their thermoelectric 
properties and their specific resistance. Thomson furthermore finds 
transversely magnetized steel electronegative towards soft steel, this again 
towaids longitudinally magnetized steel; Auerbach ("Wiedemann's ^i?iM, 
v. p. ;31(), 1878), analogously, that the specific resistance of liard steel con- 

Properties, Specijie Resistance, and Hardness of Steel. 367 

/. Like the T. E. H., so also the specific resistance of steel 
approximates to the value of this constant for soft iron. Upon 

the value found for the ratio 17. "^ , however, not much 

reliance can be placed, the factors involved being too small to 
admit of accurate determination. 

AVith cast iron no experiments were made. 

IX. Remarks on the above, considered as axLviliary to the de- 
termination of the relation between hardness and magnetic 

In this place I will avail myself of the experiments of Ruths 
on the relation between haixlness and magnetic moment, 
these being perhaps the most comprehensive. With suffi- 
cient approximation for our purjjose, we Avill put the T. E. H. 
of glass-hard rods =120 : 10^, that of the yellow annealed = 
40 : 10*^, of the blue =20 : 10^ and A^th these as abscissas and 
Ruth's values for the corresponding permanent magnetic 
moments ("in millions of absolute units," mg.-mm.-sec. 
syst.) as ordinates, suppose the curves belonging to each of 
the barst to be constructed. Tliese curves are o-iven in fijT. 6, 
the attached number referrino^ to the i*atio between the leniith 
and diameter of each rod. 

I will omit the interesting deductions which Ruths makes 
from his data, these going beyond our present purpose. 

From an inspection of the curves we derive the following 
important result, — viz. that, like the electrical properties of 
steel and its specific gravity, so also the maximum of perma- 
nent magnetism is largely modified by the different degrees 
of glasshardness of the bar («'. e. those Ipng above yellow- 
annealed and scarcely distinguishable mechanically). In the 
second place, the results of Ruths, being obtained from com- 
paratively thick bars, are largely influenced by structure. In 
view of these facts, I deem the hope by no means too sanguine, 
that, if to avoid complications from structure we experiment 
on thin rods, the maximum of permanent magnetism may be 
empiricalli/ expressed in terms of the dimensions and T. E. H. 
only — that, furthermore, from the parallelism discovered in 

tinuously increases as the rod passes from a condition of saturated loDoi- 
tudinal to a condition of saturated cii-cular magnetization. 

The result above enunciated has therefore probably even a more general 

t The data employed are those obtained by Ruths for rods 120 millims. 
long and 17, 24, 2 9, 38, 4 9, .5-9 millims. respectively in diamettir, -n-ith 
very powerful magnetizing forces. 

308 Dr. T. Canielley on the 

the variation of specific gravity and the electric properties of 
steel, the T. E. H., specific resistance, and magnetic moment 
are in some very intimate way connected with the volume of 
a unit of mass. This would imply a connexion of these phe- 
nomena with the intermolecular spaces of steel. 

In conclusion, it gives me groat pleasure to acknowledge 
my indebtedness to Prof. Kohirausch for much kind assist- 
ance throughout the course of the experiments. 

Phys. Inst. Univ. Wiirzburg, 
February 1879, 

XLI. Injlnence of Atomic Weight. B>/ Thomas Carnelley, 
D.Sc] Assistant Lecturer on Cliemistnj in the Owens Col- 

[Continued from p. 324.] 

Injiuence of Atomic Weight on the Phi/sical Properties of 

SO far, we have endeavoured to show the influence of atomic 
weight on the properties of the elements ; we shall now 
continue this subject with regard to the influence of atomic 
weight on the physical properties of compounds. 

Mendeljetf's Law of Periodicity runs thus : — " The proper- 
ties of the elements are a periodic function of their atomic 
weio-hts.'^ This law may be supplemented as follows : — '' The 
properties of the compounds of the elements are a periodic 
function of the atomic weights of their constituent elements." 
In a paper recently (June ID, 1870) read before the Eoyal 
Society the author has shown that this holds good as regards 
the melting- and boiling-points and heats of formation of the 
normal halogen compounds of the elements and of certain 
compounds of the elements with monatomic alcohol radicals ; 
and for the present we shall limit ourselves to these. 

A. Melting- and Boiling-jxyints and Heats of Formation. 

I. Normal Chlorides, Bromides, and Iodides of the Ele- 
ments. — In whatever way the melting-points, boiling-points, 
and heats of formation of these compounds be arranged, 
provided only they are arranged systematically, we always 
find that certain definite and regular relations may be traced 
between the numerical values for the above-mentioned physical 
properties and the atomic weights of the compounds. Some 
of the more important conclusions arrived at areas follows : — 

( 1 ) The melting- and boiling-points ayid heats of formation of 

Influence of Atomic Weight. 


the normal halogen compoimds of the elements are a periodic 
function of the atomic iceights of the C07istituent elements. For 
if the elements be arranged in the order of their atomic 
weights, then the melting-points, boiling-points, and heats of 
formation of tluur halogen compounds rise and fall periodically 
nine times, these periods corresponding exactly with IMendel- 
jetf's nine series of elements. The maxima occur at the posi- 
tive and the minima at the negative end of each series. 

(2) The influence of the hcdogen on these same jiht/sical pro- 
perties increases with the number of its atoms in the compound , 
thus : — 

I Br = 390* 
I CI =373 



SnBr4 = 474 
Sn CJ4 =388 

(3) In any normal halogen compound the influence of either 
of the elements on the melting- or hoiling-point increases with its 
own atomic loeight, and decreases loith the atomic weight of the 
other element. Thus : — 



Sbig =438 
SbBr3 = 363 


In each of the above pairs of compounds which contain one 
element in common the melting-point increases with the 
atomic weight of the variable element, and that whether the 
latter be the positi-se or negative constituent — thus showing 
that the influence of an element on the melting-point of one 
of its compounds increases with its own atomic weight. That 
it decreases with the atomic weight of the other element is 
shown by the following examples : — 


Aslg =419 
AsBr3 = 295 


Sbl3 =438 
Sb Bra =363 


Here the substitution of I for Br produces a larger increase 
in the melting-point in the case of the As than in that of the 

* These numbers are all reckoned from the absolute zero — 273° C. and 
this is the case with all melting-points and boiling-points subsequently 
referred to. 

370 Dr. T. Carncllcy on the 

Sb compounds, the atomic weight of As being less than that 
of Sb. Again 

Melting-point. Melting-point. 

SnBr4 = 303 


Snl, = 419 
Si I, =393 


As before, the substitution of Sn for Si produces a greater 
influence on the melting-point in the case of the bromides than 
in that of the iodides, i. e. where the atomic weight of the 
negative element is least. 

(4) The meltinf/- or hoiling-jwint or heat of formation of a 
bromide is ahcays nearer to that of the corresjyonding chloride 
than to that of the corresponding iodide; and the melting- or 
boiling-points of the lialog en compounds of the middle member of 
three consecutive elements of the same group are always nearer to 
those of the first (i. e. the one icith least atomic xoeighi) than to 
those of the last member. Thus : — 

SbCla. SbBr,. Sbl,. 

Melting-point = 345 363' 438 

Difference = 

Melting-point = 1045 

^ ._. ._ 







Difference = 

Boiling-point = 351 





Difference = 



The former of these phenomena probably depends on the 
fact that the atomic weight of Br is nearer to that of CI than 
to that of I ; and the latter on the fact that the atomic weight 
of the middle member of three consecutive elements of the 
same group is always less than the mean of those of the other 
two elements ; thus — 

CI. Br. I. 

Atomic weisht = 35-5 80 127 

Difference = 44'5 47 

P. As. Sb. 



Atomic weight = 31 75 122 


Difference =44 47 

"We have here, therefore, a good instance of the influence 
of atomic weight on the physical properties of compounds. 

Influence of Atomic Weight. 371 

(5) The melting- and boiling-points of the halogen com- 
pounds of the elements belonging to the first and second 
groups of MendeljefF's classification are widely separated from 
those of the other groups, being in fact considerably higher. 
Different relations^ too, often appear to exist between the melt- 
ing-points of even members of these two groups from those 
which exist between groups (3-7) inclusive ; while the com- 
pounds of the elements which are often placed in the odd divi- 
sions of the first and second groups are generally altogether 
irregular. In the case of the odd members of the first group, 
this may be explained by the fact that it is very uncertain 
whether Cu, Ag, and Au really belong to the same group as 
Na or not, as pointed out by Mendeljeft' in his memoir on the 
Periodic Law ; for he places these elements not in the first 
group along with Na, but in the eighth with Fe, Pd, Pt, &c. 

In the paper above referred to it has been shown how the 
preceding relations may be applied 

(1) To the calculation of unknown melting- and boilitig- 
jyoints. — The following are instances of melting-points pre- 
dicted by this method having been verified by experiment : — 

Predicted. Experiment. 

CsCl Below 959 904 \ , 

CuBr 782 777/ 

BeCl2 (820-870) (858-890) 

BeBr2 (802-820) (858-890) 

(2) To the determination of the atomic weights of elements 
when the application of the methods of specific heat and 
vapour-density are inadmissible or uncertain. By this means 
the atomic weight of Be has been found to be 9-2, thus 
agreeing with the determination of the specific heat made by 
Emmerson Reynolds, and pro^dng Xilsson and Pettersen's 
determination to be incorrect ; for they found a value for the 
specific heat corresponding to the atomic weight 13*8. 

As far as existing data allow us to judge, the compounds of 
the elements with fiuorine and also with monatomic organic 
radicals, like^vise obey the same laws as those of the halogen 
compounds. The fluorides, however, cannot be strictly com- 
pared with the chlorides, bromides, and iodides, since F is an 
even member of the seventh group ; whereas CI, Br, and I are 
odd members. 

Boiling-points of Organic Compounds in general. — The 
boiling-points and melting-points of carbon compounds de- 
pend : — (1) On the atomic weights or nature of the consti- 

* These two numbers have not been previously published. 

372 Dr. T. Carnellej on the 

tuent elements ; (2) On the position or arrangement of these 
elements in the molecule. The first of these is more especially 
rendered evident in homologous series, and the second in 
isomeric compounds. Of the latter, however, we shall have 
little or nothing to say in the present comnmnication, as it is 
intended, if opportunity admits, to refer to it at length in a 
subsequent pa})er. 

The connexion between the boiling-points and composition 
of organic compounds as pointed out by Kopp {A7171. Chem. 
Pliann. xcvi. pp. 2, 230, xcviii. pp. 267, 307) is so well known 
that it will be unnecessary to go into detail with regard to it. 
It will be sufficient to mention his more important conclu- 
sions : — (1) Analogous compounds presenting the same differ- 
ence of composition very frequently differ by the same amount 
in their boiling-points. A compound containing .rC more or 
less than another compound of analogous function generally 
boils at a temperature 29.r degrees higher or lower than the 
latter ; and if it contains .rH more or less, it generally boils 
at 5.?; degrees lower or higher. These rules are best applied 
in the case of compounds belonging to the same homologous 
series. In the fatty acids 0^ Ho^i O2 and corresponding alco- 
hols and compound ethers each addition of CH2 raises the 
boiling-point, on an average, by (29 — 2 x 5) = 19°, thus 
agreeing with the above rule. (2) An acid CraH2„02 boils 40° 
above the corresponding alcohol Cn^in+^O. (3) A compound 
ether C„H2m02 boils 82° below the acid isomeric with it. In 
other series of compounds the difference in boiling-point cor- 
responding to a difference of CHj is mostly regular ; but it is 
sometimes more and sometimes less than 19. As a rule, the 
greater the quantity of in a compound, the smaller is the 
effect on the boiling-point of an increase of CH2 in the com- 
position. In the halogen compounds of the alcohol radicals 
Cnllan+i, a difference of CH2 corresponds to a difference of 24 
to 31 degrees in the boiling-point. As an instance of boiling- 
points calculated in this way being subsequently verified by 
experiment, I give the following : — 

Calculated. Found. 

Heptyl chloride 158 159-2" 

„ bromide 179 178-5 

„ iodide 202 201-0 

.„ acetate 189 191-5^ 

Notwithstanding, however, the near agreement of many of 
the calculated wdth the experimental boiling-points, Linne- 
mann {Ann. Ch. Fliarm. clxii. p. 39), Avho has carefully de- 
* C. F. Cross (Chem. Soc. Journ. 1877, ii. p. 128). 

Influence of Atomic Weight. 


termined the boiling-points of a large number of compounds, 
concludes that the differences of boiling-point between conse- 
cutive members of homologous series are by no means exactly 
equal, but exliibit considerable variation, even as much as 3^. 

The following are a few further examples of regularity in 
the boiling-points of organic compounds which have recently 
been pointed out. 

In silicon compounds the substitution of (Cs H5) for CI 
raises the boihng-point, as does also an increase in the num- 
ber of oxygen atoms (Ladenburg, Ann. Cli. Pharm. cbdv. 
p. 300):— _ 



SiCl4 ... 58 

SiCljCCHj) ... 100 
SiCl.CC^Hj),... 129 
SiCltC/Hj),'... 144 
SiCC.Hj/ ...152 


SiCl3(C.>Hj-)0 ... 
SiCl(C., HjljO ... 
SiCC.HjXO ... 




SiCl2(C,H5),.0, ...137 
SiCl(C2Hj)3 02'...151 
Si(Co 35)^0, ...156 


SiCKC, H5)3 O3 

Si (0,35)403 


&\{C.-,B.i)^0^... 166 

Here the differences between every two consecutive mem- 
bers of each series diminish as we pass do^-n each vertical 
column, i. e. as the number of chlorine atoms replaced by 
C2 H5 increases; and these same differences also diminish in 
each horizontal line from left to ricrht, i. e. as the number of 
O atoms increases. The differences between each two conse- 
cutive members of a horizontal series increase from left to 
right, i. e. with the number Ox" atoms. 

Mendeljeff has called attention to the fact that Si com- 
pounds boil lower than the corresponding C compounds. 

The iodides of the alcohol-radicals always boil 53° higher 
than the con-esponding amides (Linnemann, Ann. Ch. Pharm. 
clxii. p. 12), thus : — 

Ethyl. 1 Propyl. 


■'»'"■'."•' "^s;!:' ^■°>'- 







126-6 98-5 
67-5 460 


^'H,= ... 


53-3 53-2 


531 525 


Salomon {Journ. f. Chem. [2] vi. p. 433) has shown that 
Phil. Mag. S. 5. Vol. 8. Xo. 50. ^^ov. 1879. 2 C 


Dr. T. Carnellcy on the 









in the case of the ethyl carbonates and ethyl sulphocarbonates, 
the introduction of an atom of S into the ethylated radical is 
accompanied hy a rise of 40° in the boiling-point, and by a 
rise of 44° when the S is introduced into the carbonyl group, 
except as regards the tirst member of the series : — 

Boiling-point... 125° 15G° 

Boiling-point ... 200° 

From the following Table it is seen that an ethereal salt of 
a In-droxv-acid boils 20° higher than its methoxy derivative, 
and that the ethyl salts of a hydroxy- and an ethoxy-acid have 
nearly the same boiling-point. Further, the boiling-point of 
an ethereal salt rises 20° for the first addition of CHj to the 
alcohol-radical and 26° for the second ; but only 6° and 8° 
respectively for a similar addition to the saline radical 
(Schreiner, Ber. dent. chem. Ges. xii. p. 179). Again, the 
meth3'l and ethyl acids boil exactly 40° higher than their cor- 
responding ethyl salts. 







C2H5. C3H,. 




«,-• fOH ... 

I.i CH,... 
-5 ^ 1 C2 Hj.. 













OH. CH3. 




|.l |CH,... 

"^ Ic;h;.. 






Those benzene hydrocarbons containing an even number 
of methyl groups are solid, whereas those containing an odd 
number are liquid, or melt very much lower. The difference 
between the boiling-points also changes periodically from 30° 
to 25° (Jannasch, Ann. Chem. clxxvi. p. 283). These facts 
are probably due to the circumstance that in those hydrocar- 
bons containing an even number of methyl groups the latter 

Influence of Atomic Weight. 


are symmetrically arranged; whilst in those containing an 
odd number the arrangement is generally asymmetrical. 





Cg H3 (0113)3. 


Melting- ] _ 
point. J 

Boiling- "1 _ 
point. J "~ 






Groebe (^Ber. cleut. chem. Ges. vii. p. 1629) has shown that, 
as a general rule, diphenylene compounds boil 40° higher than 
the corresponding compounds of diphenyl, phenanthrene alone 
being an exception ; thus : — 





1 >o. 



1 >H,. 

Boiling-] _ 
point. J 





As regards the boiling-points of isomerides, Naumann 
{Ber. cleut, chem. Ges. vii. pp. 173, 206) has pointed out 
that the simple chain formulse allow of greater condensation 
of the molecule, and consequently give a higher boiling-point ; 
whilst the more this form is disturbed by side chains, the 
lower the boiling-points. Also, the boiling-points of meta- 
merides of analogous constitution and containing 0, are the 
lower the nearer the is to the centre of the chain of atoms ; 

thus : — 

Butyl alcohols , 

— ICH3 

Methylpropyl ether... CH3, 
Diethyl ether CH3 

CH2 CB, . CH2 
CH2 . . CH2 . CH3 


OH 116 \ 
99 j 

The theory has been advanced by Burden (Phil. Mag. [4] 
xli. p. 528) that at the boiling-point (Bar. = 760) the velocity 
of the molecules is a constant for all liquids, viz. =1140 feet 
per second. This number is obtained by the use of the equation 

V Cat b.-p.)= ^73 + b.-p. /Tvelocity of H gasl^U)^ 
^ 273 V vapour-density of the liquid ' 

the velocity of H at 0° C. being =6050 feet per second. For 
the raison d'etre of this equation, reference must be made to 
the original paper. Burden gives a large number of Tables 


37G Dr. T. Carnelley on the 

in support of his view. The following arc the mean veloci- 
ties calculated by him for several series of compounds : — 

Paraffins 1138 feet per second. 

Olefines 1155 „ ,, 

Other hydrocarbons 1182 „ „ 

Aromatic hydrocarbons... 1243 „ „ 

Simple ethers 1131 „ „ 

Methylic salts 1185 „ „ 

Ethjdic salts 1140 „ „ 

Other ethereal salts 1125 „ „ 

Anhydrides 11G7 „ „ 

The alcohols and acids, however, give a much higher velo- 
city (1300-1800 feet per second) at their boiling-points than 
the above. But it is probable that these compounds arc not 
so exceptional as might at first sight appear ; for the acids of 
the series Cn H^n O2 exhibit a remarkable variation in the 
volume-vapour which they furnish at different temperatures 
(Bineau). Thus, formic acid at its boiling-point (101°) has a 
vapour-density of 46 in place of 23, and gains its proper bulk 
only at 213°. A similar thing also applies to acetic acid. If, 
therefore, these facts be taken into consideration, formic acid 
will show at its boiling-point a velocity of IIGO feet, and 
acetic acid a velocity of 1134 feet per second. Herwig has 
shown that ethyl-alcohol also possesses an exceptional vapour- 
density at or near its boiling-point. 

Pictet has recently pointed out (Compt. Rend. Ixxxviii. 
pp. 855, 1315), as already stated, that there exists a simple 
relation between the atomic weight, coefficient of expansion, 
and melting-point of a solid body*. He also finds that a similar 
relation {Compt. Mend. Ixxxviii. p. 1315) exists between the 
atomic weight, coefficient of expansion, and boiling-point of 
a liquid ; thus : — 

(1) The length of oscillation of liquid molecules at the 


V p 

(2)/T = Kn; 

where a = mean coefficient of expansion between the melting- 
and boiling-points, f? = density, /; = constant, T = boiling-point 
reckoned from —273° C, ^^ = th'e physical molecular weight, 
?'. e. those weights of different liquids Avhich absorb equal 
quantities of heat on their temperature being raised from 0° 
to 1° C. ; and this, being inversely as the specific heat, is a 

* See also a paper by "Wiebe ou ibis subject in the Chemical Jsews for 
September 26, 1879, p. 154 

Influence of Atomic Weight. 


simple multiple of the chemical or true molecular weight ; n 
is a number proportional to the number of liquid molecules in 
a given unit of length. 

Melting-points of Carbon Compounds in general. — But little 
attention has been directed to the influence of atomic ^Yeight 
on and the relations bet^Yeen the melting-points of carbon 
compounds. It is, however, a subject which would no doubt 
repay careful investigation, and is especially important from 
the fact that this physical property is the one which renders the 
most service in the recognition of the solid compounds of 
carbon. The following relations will be of interest. 

As pointed out above in speaking of boiling-points, those 
aromatic hydrocarbons containing an even number of methyl 
groups are solid, whilst those containing an odd number are 
liquid. A similar thing applies to the chlorine, and doubtless 
to other derivatives of benzene 5 for those containing an odd 
number of 01 atoms melt much lower than those Avith an 
even number, thus : — 

CeHfi. CeHs.Cl. 



CeH,.Cl,. CfiH.CV 



Melting- 1 _ 
point. J ~ 



53° 17^ 


139" 74'^ 


The difference between those compounds containing an odd 
number of CI atoms is constant, viz. 57°, and also the differ- 
ence befween those containing an even number of CI atoms, 
viz. %(i°. These facts, as previously intimated, probably de- 
pend on the symmetrical or as^onmetrical arrangement of the 
CI atoms. 

As a general rule, the melting-points of a series of homo- 
logous compounds rise as we ascend in the series ; but there 
is one remarkable case known in which the reverse is the 
thus : — Melting-point. 
Methyl terephthalate 140 









The relations between the melting-points of organic com- 
pounds and their chemical composition offer so wide a field of 
investigation, and one which has been so little touched, that 
it is my intention at an early date to trace these reh'tions as 
completely as possible, especially as regards the influence of 
the position of the atoms, and more particularly with respect 
to the influence of symmetry. I have ah-eady worked a good 

378 Dr. T. Carnelley on the 

deal at this subject, and have come to the following conclu- 
sions : — 

(1) The melting-points of those compounds the atoms of 
which are symmetrically arranged, are higher than in the case 
of compounds in which the atomic arrangement is asymme- 
trical. (2) The stability (and therefore the heat of formation) 
of symmetrical compounds is greater than that of asymme- 
trical compounds isomeric with them. If this be true, then 
it would follow that the heats of combustion of the former 
compounds are less than those of the latter. 

The application of the first of these conclusions may be 
made, first, to isomeric compounds, and, secondly, to com- 
pounds belonging to the same homologous series ; whilst the 
second refers of course only to isomeric compounds. I re- 
sen-e, however, the details of this investigation for a future 
communication. Since working this subject out at some 
length, I have noticed that Mr. Henry Watts, F.R.S., in the 
last Supplement (vol. viii. p. 221) of his ' Dictionarv of Che- 
mistry ' has shown in a very clear and decisive manner that 
" The more symmetrical the constitution of a benzene deriva- 
tive, the greater is the resistance which it otters to the passage 
from the solid to the liquid state," or, in other words, the 
higher the melting-point. 

Freezhtg-points of Saline Solutions. — De Coppet (^Ann. 
CJiim. PJnjs. [4] xxiii. p. 366, xxv. p. 502, xxvi. p. 98) has 
shown, as the result of a long series of experiments, that for 
bodies heloncjing to the same molectdar gro^q) the coe^dent of 
depression of the freezing-point is inversely/ as the molecidar 
iceight ; i. e. the molectdar depressions of the freezing-point are 
equal. A similar relation also exists between the molecular tceights 
of salts and the loicering of their temp^eratures tf maximum den- 
sity, and affords for the solutions of a large number of salts 
the means of calculating the temperature at which they freeze, 
and also that at which they possess a maximum density. For 
a large number of bodies also the molecular depression of the 
temperature of maximum density is nearly four times as great 
as the molecular depression of the freezing-point. The first 
of these statements is illustrated as follows : — 


Coefficient of 



depression of 



freezing-point, h. 



,. 74-6 


34-8 > 


,. 119-1 



,. 166-0 


KNO3 .. 

,. 101-0 


27-0 \ 


,. 85-0 


Influence of Atomic Weight. 379 

Eaoult (Compt. Rend. Ixxxvii. p. 167) has further shown 
that the property which anhydrous saUs possess of diminish- 
ing the vapour-tension of their solutions and of lowering their 
solidifying-point appears to be iuyersely as their molecular 

Division of a Body between tico Solvents. — From his experi- 
ments on the division of a body between two solvents, Ber- 
thelot {Ann. Chim. Phijs. [4] xxvi. p. 408) concludes, with 
regard to the relations between the coefficient of division and 
the chemical composition of the substance dissolved, that ether 
removes from water with greater fticility : — (1) the more 
highly carburetted of two homologous acids; (2) a monobasic 
acid more easily than the corresponding dibasic acid, as acetic 
rather than oxalic ; (3) a monobasic acid rather than a dibasic 
acid of nearly the same composition, as acetic rather than 
succinic. (4) Of two acids containing the same proportion of 
carbon and hydrogen, that with the smallest number of 
atoms is the more easily removed, as succinic, Q Hg O4, 
rather than mahc, C4 Hg O5, or tartaric, C^ Hg 0^. 

Ttr 1 1 o ■ - Tr 7 / molecular weightx 

Molecular or bpecifio Volumes i = r^ r— ). — 

■^ -^ \ specinc gravity / 

Schroeder (Pogg. Ann. clx. p. 199) has proposed the h}-po- 
thesis that "All bodies combine in whole volumes." In the 
case of gaseous bodies this can be proved, as is well known, 
without exception by reducing to a common temperature and 
pressure (Gray-Liassac). For liquids, Kopp {Ann. Chem. 
Pharm. xcvi. pp. 153, 303) has sho\\ii that the volumes of 0, 
H, 0, and other elements in organic liquids are equal in all 
compounds if their specific gravity be determined at the 
boiling-point. The following are his more important results : — 
(1) Differences of molecular volume are proportional to the dif- 
ferences between the corresponding chemical for nudce. Thus the 
difference of CH2 in homologous series corresponds to a dif- 
ference of 22 in the molecular volume, thus : — 

Molecular Specific 

weight. volume. Difference. 

Formic acid 46 42 — 

Acetic „ 60 64 22 

Propionic acid 74 86 22 

Butyric „ 88 108 22 

(2) Isomeinc liquids belonging to the same chemical type have 
equal molecular volumes. Thus ^ ^H I ^ ^^^ CH^ I ^ 
have the same molecular volume, viz. 63*4. (3) Compounds 
containing as many times two atoms o/'H less^ as others contcdn 

380 Dr. T. Carnelley on the 

one atom of C more, have the same molecular volume ; or, the 
volume of one atom of C is equal to that of two at0)ns ofK 
thus : — 

Molecular Molecular 

weight. volume. 

rCg His 114 187 

\CioHi4 134 187 

/C,HioO 74 106-8) 

ICcHgO 94 100-8/ 

Now it has already been shown that the volume of CH2 = 22; 
therefore the specific volume of C = ll, and that of H = 5-5. 

In liquids belonoring to different types, the volume of the 
oxygen varies according to the manner in which it is com- 
bined in the compound. When the is joined on to C by 
one combining power only, its specific volume =7-8; but 
when attached to C by both its combining powers, its specific 
volume =12*2. A similar thing occurs in the case of S: its 
specific volume in the former case being 23, and in the latter 
28-6. The specific volume of Cl = 22-8, of Br=27-8, of 
1 = 37-5. N in ammoniacal compounds =2*3, in cyanides 
= 17-0, and in nitro-compounds =17--4. By the use of these 
constants we may calculate the molecular volume of a com- 
pound when its molecular formula is known, thus : — 

Calculated. Found. 
H2O =2x5-5 + 7-8 = 18-8 18-8 

C2H5. OH =2x11 + 6x5-5 + 7-8 = Cy2-8 62-5 

CO. (CH3)2 = 3x 11 + 6x5-5 + 12-2= 78-2 77-6 

C6H5.NH2=6x 11 + 7x5-5+ 2-3=106-8 106-8J 

It appears then that the molecular volume depends not 
only on the chemical composition, but also on the constitution 
or arrangement of the atoms in the molecules. 

As regards the molecular volume of solids, Kopp (Pogg. 
Ann. xlvii. p. 133; lii. pp. 243, 262), and more especially 
Schroeder (ibid. 1. p. 552, lii. pp. 269, '2S2, cvi. p. 226, 
evii. p. 113), have endeavoured to show that the hypothesis 
that all bodies combine in whole volumes holds good not only 
for gases and liquids, but also in the case of solids ; and 
Schroeder has pointed out that "equivalent quantities of different 
elements in uniting toith the same quantity of a given element 
(or compound radical) receive equal increments of volume. ^^ The 
explanation of this appears to be that certain elements enter 
into combination with the same volume which they occupy in 
the free state. More recently Schroeder (Deut. chem. Ges. 

* Schorlenuner's ' Chemistry of the Carbon Compounds.' 

Influence of Atomic Weight. 381 

Ber. vii. p. 676, ix. p. 1188, x. pp. 848, 1871, xi. pp. 1109, 
1U2, 2017, 2128, xii. p. 119; Po.irg. Ann. clx. p. 199) has 
shown that when an element Hke silver and a series of its 
compounds have volumes which stand exactly to one another 
in simple relations, then they have equal volume-masses or 
equal steres. Every volume may in fact be represented as a 
simple multiple of a common volume-mass or stere. So that, 
"/n every solid compound the volume-measure or stere of one of 
its elements determines all the other components, and causes 
equal volume-measures to talce up equal steres.''' In other words, 
one of the elements of a compound impresses its own volume- 
mass or stere on the whole compound, and becomes the con- 
trolling element in a whole series of otherwise very different 
compounds. Thus : — 

Calculated Observed 
volume. volume. 

Ag2 = 2x5-14 = 10-28 =10-28 

Ag^Cl^ = 5x5-14 = 25-70 =25-70 

Ag?Br^ = 6x5-14= 30-84 =30-84 

Agflf =8x5-14=41-12 =41-12 

In the above examples the number of atoms in a compound 
is indicated in the usual way by a number placed to the right 
and under side of a symbol, and the number of its steres by a 
number at the right of the upper side. Here in these com- 
pounds it is seen that silver is the predominating element; 
for it impresses its stere ( = 5-14) on all the other compounds. 
By the use of this law Schroeder has endeavoured, with some 
success, to determine the molecular weight of a solid body ; 
for if substances combine only in whole ^'olmnes, then the 
molecule of a body must contain the number of atoms which 
are necessary for the components of the compound to fill 
the space of the whole number of volume-units. He also 
shows that in many compounds which are capable of existing 
in more than one form, the difference in form depends on 
which is the dominating element in the compound. Thus 
black cinnabar is distinguished from the red by the fact that 
in the former the mercury stere dominates, whilst in the latter 
it is the sulphur stere. 

[To 1)6 continued.] 

[ 382 ] 

XLII. On the Tension of Vapours near Curved Surfaces of their 
Liquids. By Geo. Francis Fitzgerald, M.A., F.T.C.D,* 

SIR W. THOMSON showed, in the Proc. Eoy. Soc. of 
Edinburgh, Feb. 7, 1870, that the maximum tension of a 
vapour at the curved surface of its liquid when convex was 
greater, and when concave less than when flat. He deduced 
this as a consequence of the ascent of liquids in capillary 
tubes, bj pointing out that the tension of vapour at the top 
and bottom of the column of liquid differs by the weight of a 
column of the vapour of that length, while it is impossible to 
suppose that there can be a continual distillation from the flat 
surface of the liquid to the curved one in the tube. He does 
not seem, however, to have observed how this result is con- 
nected Avith the ordinary theories of evaporation; and it is this 
connexion which I desire to point out. 

Assuming, as seems very probable, that evaporation is due 
to the escape of molecules of the liquid, not from the surface 
only, but from a very small depth indeed beneath it as well, 
and that the chances of escape are less the longer the path of 
the molecule within the liquid, it is at once obvious that a mo- 
lecule situated at a given depth below the surface will have a 
much better chance of escape if the surface be convex than if 
it be flat, and better still than if concave. On the other hand, 
one tending to enter the liquid from a given depth in the va- 
pour has a less chance of entering a convex surface than a flat 
one, and still less than of entering a concave one. Hence, in 
order that the equality between the numbers entering and 
leaving the surface may be maintained (i. e. in order to pre- 
vent either evaporation or condensation), the tension of the 
vapour would have to be greater when in contact with a con- 
vex surface than when in contact with a flat, and still greater 
than when in contact with a concave surface. 

If the matter be investigated mathematically, it may be treated 
very generally indeed if we assume that the depth from which 
evaporation takes place is so small compared with the radii of 
curvature of the surface of the liquid, that powers of the ratio 
of the former to the latter above the first may be neglected. 
This is certainly legitimate in all cases that can be observed ; 
for the depth from which evaporation takes place must be very 
small indeed compared with the radii of curvature of the sur- 
faces with which we have to deal. 

* Communicated by the Author, haviug been read at the Meeting of 
the British Association in Sheffield, 

Tension of Vapours near Curved Surfaces of their Liquids. 383 

Let, then; the equation of the surface referred to its tangent 
plane be 

a o 

where a and h are consequently the principal radii of curvature 
at the point, and the higher powers of :c and y are neglected ; 
for it is obvious that it is only points near the origin that are 
of any importance. Now z is to be very small, so that x^ and 
y^ are small compared with a and h. Let r be the radius 
draAvn from a point situated on ^ at a very small distance 7 
from the origin to any point on the surface, and let 6 be the 
angle between this radius and the normal at the point where 
it meets the surface, and i/r the angle between this normal 
and z. A molecule then emitted from 7 in the direction v 
"svill have to travel a length r within the liquid before escaping. 
Let then /(?•) represent the numbers emitted after having tra- 
velled this distance ^vithin the liquid. All that we know of 
/(?') is that it vanishes for all values of r above a very small 
quantity. Hence we may express the numbers emitted from 
this point by the double integral 

*/(/') cos 6 dd'dy _ 
r' cos xjr ' 

and bearing in mind that a and b are large compared with such 

values of r, x, y, and 7 as do not make /(j-) to vanish, we can 
evidently expand this into the form 



where Aq, Ai, Bi are functions of x, y, and 7. It is now to 
be observed that, on account of the symmetry of the equations 
involved in x and y, we must have 


and that, consequently, the numbers escaping from this point 
may be expressed as 

?l = ^0 + 111 


and if this be integrated for all depths y, as a and 5 are the 
same for each the result must be of the same form, and may 
be written 

N=No + 


In this No is the number that would be emitted if the surface 
were flat; and by changing the signs of a and h we get the 

384 Tension of Vapours near Curved Surfaces of their Liquids. 

case of a surface GurveJ in the opposite direction. From tlie 
considerations mentioned in the beginning of the paper, it is 
obvious that Ni must be positive when the surface is convex. 
In order to obtain the numbers admitted to the surface, wo 
should have to substitute in the foregoing investigation the 
function corresponding to vapour for /'(/•) that corresponds to 
tlio liquid ; but the rest of the investigation is the same, it 
being recollected that when the surface of the liquid is convex 
that of the vapour is concave, and r>ice vei'sd. Hence in the 
case of a convex liquid surface, we may write those emitted as 

and those admitted as 


and for equilibrium we must have 

In discussing this result, it is to be observed that an increase 
in the tension of the vapour probably produces little or no 
effect upon the numbers emitted, and that consequently Nq 
depends only upon the nature and temperature of the liquid ; 
and it is the number that would be emitted or admitted if the 
surface were flat, and the tension the maximum corresponding 
to its state. On the other hand, the change in the numbers 
that would be admitted to a flat surface is proportional to the 
change in tension at that surface; so that changes in N'o are 
proportional to the changes in tension of the vapour. AVe thus 
at once conclude that the maximum tension of vapour in con- 
tact with a convex surface of a liquid must be greater than 
that at a flat one by a quantity which varies directly as the 
sum of the curvatures of the surface. We know from Sir W. 
Thomson's investigation, that the coefficient by which this sum 
of curvatures is multiplied is proportional to the tension of the 
surface of the liquid ; and we can thus connect tAvo apparently 
unrelated quantities, namely the rate of evaporation with the 
superficial tension. As f(r) is the only unknown in the fore- 
going investigation, it might be possible to determine it by 
observing the rates of evaporation from drops of various sizes. 
That the tension of the vapour was connected with the sum 
of the curvatures might also have been suspected from the 
equilibrium of the surface requiring the normal pressure to 
vary with this same sum. 

[ 385 ] 

XL III. The Pseudophone. By SiLVAxrs P. Thompson, B.A., 
D.Sc, Professor of E.vperimental PIvjsics in Universitij Col- 
lege, Bristol*. 

THE Pseudoplione is an instrument for investigating the 
laws of Binaural Audition bj means of the illusions it 
produces in the acoustic perception of space. It is therefore 
the analogue for the ears of the Pseudoscope of Wheatstone, 
which serves to illustrate the laws of BinocularYision b j means 
of the illusions it produces in the optical perceptions. 

The author has for some months been occupied A^th an ex- 
perimental and theoretical investigation of the question of 
binaural hearing, the chief points hitherto considered being 
the subjective perceptions of two sounds led separately to the 
ears, and differing in pitch, phase, or intensity. The results 
of these investigations v>-ere communicated to the British 
Association in the years 1877 and 1878, and have been pub- 
lished in the Philosophical Magazine for 1877 and 1878. 

Independently of the work of the author, the theory of Bin- 
aural Audition has been attacked by Prof. Anton Steiuhauser 
of Yiennat, who has, however, ti-eated the subject from a 
somewhat different point of view, and has carefully developed, 
by geometrical and algebraic reasoning, the laws of the rela- 
tive intensities with which sound-waves reach the ears from 
sources of sound situated at various points in front, or at the 
side, or back, of the observer. In thus calculating accord- 
ing to known geometrical laws the intensities of sounds which 
reach the ears. Professor Steinhauser neglects such accessory 
effects as might be produced by differences of pitch, or tUffer- 
ences in phase, or diversity of quality of the sounds, and 
assumes that these have nothing to do with the acoustic per- 
ception of the direction in which a sound hes. He assumes 
that that perception is based solely upon the relative intensi- 
ties of the two sounds ; and upon this assumption his conclu- 
sions are indisputable, being simply geometrical deductions 
from the postulates of the problem. 

The author has, however, shown that differences of pitch 
and of phase play a very important part in the subjective phe- 
nomena of audition. His experiments with the simple tones 
of tuning-forks, which were transmitted by mechanical or 
electrical means to the ears in such a manner as to produce 
required differences of phase, showed that difference of phase 

* Communicated by the Author, having been read before Section A of 
the British Association at Sheffield, August 22, 1879, 

t Vtde Stekilaauser, "Theory of Binaural Audition," Phil. Mag. April 
and May 1879. 

386 Prof. S. P. Thompson on the Pseudophone. 

influences the perception of the direction of a sound in a sin- 
gular manner. Moreover, since the sounds issuing from a 
])oint to the right or left of the hearer travel paths of unequal 
length to the two ears, the difference of phase thereby caused 
in the two perceived sounds will depend also upon the wave- 
length of the sound or on its pitch, if simple ; and the result 
will be still more complex if the sound be not a simple tone. 

Again, Lord Rayleigh has shown reason for thinking* that 
the diffraction suffered by the waves of sound as they travel 
round the head of the observer to the two ears will affect 
sounds of high and low pitch very unequally, and Avill there- 
fore still further complicate the perception of the direction of 
a sound by causing the quality of the sound, if compound, to 
vary with the position of the head with respect to the direction 
of the sound-waves, since in different positions the intensities 
of the high and low components would be differently affected 
as to their intensity. 

These considerations tend to throw some doubt upon the 
reasonableness of the assumption made by Prof. Steiuhauser, 
in referring the perception of the direction of sounds to the 
perception of their relative intensities. His conclusions are 
in fact too general, and can only be considered applicable to 
certain cases not complicated by questions of pitch or quality, 
or by the influence of diffraction. 

In order to obtain a definite idea of the degree of trustwor- 
thiness of the results so carefully elaborated by Prof. Stein- 
hauser, the author undertook a series of experiments on the 
perception of the direction of sounds of different kinds and 
pitches, which are not yet concluded — but which at present 
tend to show the unexpected result that Steinhauser's theory 
is approximately true for sounds of high pitch only, and not 
for sounds of medium or low pitch, and that it is more nearly 
true for sounds in front of or behind the observer than for sounds 
which reach him obliquely from right or left. 

In the course of these researches, it occurred to the author 
that a simple means of testing some of the main features of 
the theory was afforded by the possible production of acoustic 
illusions, making sounds appear to come from other directions 
than the real source. For if the perception of the direction of 
a sound depends upon the relative intensities with which it 
reaches the two ears, and if the intensities with which the sound 
is perceived in the two ears depend, as Steinhauser assumes, 
upon the effective magnitude of the pinna or external flaps of 
the ears and upon the angles which they make with the line of 
sight, then any device which should virtually alter either the 
* ' Transactions of Musical Association/ 1876. 

Prof. S. P. Thompson on the PseudopJione. 387 

effective magnitude or tlie angle of the pinnse to an amount 
unknown to the observer must produce a false perception of 
the relative intensities of the sounds, and give rise to an illu- 
sion as to the direction of the sound. 

The simple instrument for 
which the author suggests the 
name PseudopJione consists of 
a pair of ear-pierces^ A A, fur- 
nished with adjustable metallic 
flaps or reflectors of sound, C C, 
which can be fitted to the ears 
hj proper straps, D and E, and 
can be set at any desired angle 
with respect to the axis of the 

ears, and can also be turned 

upon a revolving collar about 

that axis so as to reflect sounds into the ears from any desired 


The theory of the Pseudophone is very simple, and is as 
follows : — 

The intensity of a perceived sound depends upon the amount 
of space over which the waves are gathered by the external 
collecting apparatus of the ear ; and by analogy with optical 
phenomena we may say it depends upon the number of rays 
of sound which reach the ear. 
Let the effective surfaces of the 
pinnse which gather the sound- 
rays be /i and /g, and let them 
make equal angles (f)i and <^2 '"'ith 
the line of -sasion. Let the rays 
of sound that reach the ears fall 
in a direction indicated by the 
lines S, S, S, making an angle 9 
with the line of sight. The lines 
m and n, which are drawn per- 
pendicularly, measure the num- 
ber of sound-rays which reach 
the pinna?, and are therefore pro- 
portional to the intensities of the 
sounds which reach the ears. 




=/isin(^ + ^), 
n=f2sm((f) — e); 


388 Prof. S. P. Thompson on the Pseudophone. 

:uul, developing the sines, 

m _/i sin 6 cos </> + cos sin ^ 
n /o sin (^ cos ^— cos sill ^ 
Divide by cos ^ cos ^, and reckon /i=/2. 
■m _ tan ^+ tan </>. 
?i tan (^ — tan 6 

171 + n _ tan <^ 
m — n " tan ^ 



tan ^= tan (b. 

m + 11 

/. tan 6= -^ — ^ tan <f>. 

^1 + 22 ^ 

Or the difference of the intensities as compared with their sum 
affords a means of comparing the angle between the line of 
vision and the direction in which the sounds come, with the 
angle made by the effective surfaces that receive the raj'S of 

Such an estimate as we are therefore able to make of the 
position of a source of sound, judging solely by the relative 
intensities of the sensation in the two ears, depends upon our 
previous perceptions and upon our possession of a constant 
amount of effective auditory surface, and a constant angle 
subtended between the ears and the line of vision. 

In the Pseudophone these angles are variable, and the 
amount of effective surface can also be varied, and this with- 
out any knowledge, on the part of the person experimenting 
with the instrument, as to how much they may be varied. 
Hence the acoustic illusions which are now to be described. 

* This equation, which is the starting-point of Steinhanser's theory, 
ought more strictly to be interpreted thus : The ratio between the differ- 
ence of the intensities and their sum is the same as the ratio between the 
tangent of the angle between the line of vision and the direction in which 
the sounds come and the tangent of the angle made by the effective sur- 
faces that receive the soimd with the line of vision. Steinhauser assumes, 
as it is assumed in the paragraph above, that the ratio between the tan- 
gents of the angles will be the same in our perception as the ratio between 
the angles themselves. This is, of course, only true when the angles are 
very small. Only, uufoilunately, for very small angles the perception 
ceases to be very accurate. No experimental determinations of the degree 
of accuracy of perception have yet been published. 

Prof. S. P. Thompson on the Pseudophone. 389 

Suppose one flap to be adjusted at an angle of about 40 
degrees with the line of sight, in which position it is about 
most favourably situated to receive sounds from a point right 
in front of the observer; then if the other flap be adjusted to 
any angle greater or less than 40°, fewer ra}-s of sound are 
reflected into the ear on that side than on the other, and the 
hearer imagines the source of sound to be situated on that side 
on which the sensation is more intense. Accordingly, to verify 
the perception, the hearer turns his head until both ears hear 
the sound equally loudly, and imagines then that he is looking 
in the direction of the sound, whereas he is looking at a point 
situated nearer to that side on which the larger eftective sur- 
face exists. This observation agrees with Steinhauser's theory. 
The illusion is very easily obtained by means of a loud-ticking 
clock, but with some persons does not succeed unless their 
eyes are blindfolded ; for when there is a conflict between the 
evidence of the eyes and the evidence of the ears, the tendency 
appears to be to believe the former rather than the latter. 

A more striking illusion occurs when the flaps of the pseu- 
dophone are reversed and adjusted so as to reflect into the ears 
sounds which come from immediately behind the obser\^er. 
In this case also, if a source of sound, situated anywhere be- 
hind the head, be observed, if the observer does not know how 
the flaps are adjusted, he will estimate it to be somewhere in 
front ; and, on turning his head about until the sounds are 
equally intense, he judges himself to be looking straight at the 
source of sound, whereas it is in reality exactly in an opposite 
direction. This illusion succeeds well with a loud-ticking 
clock, well also with the human voice, but not well with a 
tuning-fork of medium pitch. In a room the experiment may 
succeed with a tuning-fork ; but there is never the same clear 
and decisive impression as to the position of the sounding 
body. In the open air the writer has never succeeded in pro- 
ducing the illusion with a tuning-fork ; for the sensation is one 
of a character from which it appears to be impossible to draw 
any precise judgment. The sound does not appear to have 
any precise locality. This result, which agrees with some 
experiments made by Lord Eayleigh with tuning-forks, stands 
in strong opposition to Steinhauser's theorv, which ouo-ht, if 
true at all, to be a fortiori true for simple sounds. The author's 

experiment differs from that of Lord Eayleigh in this respect 

that in the case of Lord Eayleigh's experiments with the un- 
aided ears the head of the observer was to be held immovable; 
whereas in the experiment with the pseudophone the head is 
turned about, seeking in vain a direction which can be pro- 
nounced to be that of the sound-rays. 

Fhil. Mag. S. 5. Vol. 8. No. 50. Kov. 1879. 2D 

390 Dr. W. Spottiswoode on a Mode of 

The illusion succeeds in the open as well as in-doors with 
the sound of u loud-tickinf^ clock, and with the human voice ; 
but with shrill sounds it succeeds best, notably with the sharp 
click of a metronome, and even Avith a metronome-bell. 

These results point to the explanation foreshadowed by- 
Lord Raylei»h, namely that the diffraction of sounds of medium 
and great wave-length around the head, thus bringing the 
lower and upper partial tones of the compound sound in un- 
equal intensity to the two ears, plays a great part in our per- 
ception of the direction of sounds. When the effects of dif- 
fraction are such as to be relatively negligible, as for shrill 
sounds (whose wave-length is small) , then Steinhauser's theory 
of the relative intensities appears to hold good. Any one may 
at once convince himself of the fact that diffraction may thus 
produce a difference in the relative intensities with which the 
partial tones of a complex sound reach the ears, by the simple 
experiment of comf)aring the note of a musically-ticking clock 
placed in front of the head with its note when placed behind. 
They appear somewhat different, the difference being one of 
timbre rather than of total loudness. 

Another experiment with the pseudophone which gives rise 
to acoustical illusions, consists in setting one flap to catch sounds 
from the front, while the other catches sounds from behind 
or above the observer. Under these circumstances the sounds 
seem, as the observer moves his head, to come sometimes from 
the right, sometimes from the left, or sometimes from the 

Lastly, most of these experiments with the pseudophone can 
be repeated simply by holding the hands in front of the ears 
as flaps ; but here the illusion does not always succeed, as the 
observer is conscious that his hands are reflectino- to the ear 
sounds from a certain direction, and so the judgment is sophis- 

XLiy. A Mode of Exciting an Induction-coil. By William 
Spottiswoode, M.A., LL.D.^ President of the Royal Society. 

To the Editors of the Philosophical Magazine and Journal. 

IHAV'E lately tried a mode of exciting an induction-coil, 
which I have not seen elsewhere described, and Avhich 
appears to promise valual)le results. It consists in connecting 
the primary circuit directly with a dynamo- or magneto-machine 
giving alternate currents. In my own case I have used one 
of M. de Meritens's excellent machines driven by a three-and- 
a-half horse-power Otto silent gas-engine. The speed of the 

Exciting an Induction-coil. 391 

De Meritens machine so driven is about 1300 revolutions per 

In this arrangement the "make" currents are of course 
alternately in one direction and in the other, as also are the 
"break" currents; so that the discharge appears to the eye 
durino; the workino- of the machine the same at both termi- 
nals of the tube. 

The advantages of the method are : — first, the fact that, as 
the machine elfects its own make and break, both the contact- 
breaker and the condenser of the induction-coil can be dis- 
pensed with ; secondly, that the breaking of the primary, 
and consequently the delivery of the secondary, currents is 
perfectly regular ; thirdly, that the quantity of the currents 
in the secondary is very great. With a 20-inch coil by Apps 
I have obtained a spark about 7 inches in length, of the full 
thickness of an ordinary cedar pencil. But for a spark of 
thickness comparable at least with this and of 2 inches 
length an ordinary 4-inch coil is sufficient. 

Omng to the double currents, this spark consists of a bright 
point at each terminal, and a tongue of the yellow flame, such 
as is usually seen with thick sparks from a large coil, issuing 
from each. There is no spark proper during the undisturbed 
passage of these flames ; but if the latter be blown aside, a 
stream of true bright-line sparks is seen passing between the 
terminals. This torrent of flame (which, owing to the rapidity 
with which the currents are delivered by the machine, is ap- 
parently continuous) may be maintained for any length of 
time. It would seem more than probable that this spark may 
give some very valuable results in spectrum-analysis. The 
sparks resemble those given by my great coil (described in 
Phil. Mag. 1877, vol. iii. p. 30) with large battery-power and 
with a mercury break ; but with that instrument it is doubtful 
whether such thick sparks could be produced at short intervals 
or in a rapid shower as in this case. 

In vacuum-tubes, exhausted so as to show bulbous striae, 
the effect is excellent. The strijB appear perfectly steady, as 
with a battery like Mr. Gassiot's or Mr. De la Rue^s : and 
their brilliancy and configuration can be controlled by means 
of a shunt in the secondary circuit, formed of a column of gly- 
cerine and water, so as to diminish at will the amount of current 
flowing towards the tube. 

But I postpone an account of various experiments made with 
this method until a future occasion. 

I am, Gentlemen, 
Sevenoaks, Yours faithfully, 

September 20, 1879. W. SpoTTISWOODE. 


[ 392 ] 

X LV. On a new Standard of Light. By Louis ScHWENDLER*. 
[Plate XI. figs. 7-10.] 

NO exact measurement of any quantity, even with the 
most accurate and sensitive test-methods available, can 
reasonably be expected unless the standard by which the un- 
known quantity is to be gauged is perfectly constant in itself ; 
or, if nature does not permit of such a desirable state of things, 
the causes to which the variation of the standard are due 
should be known, and in addition also their quantitative effect 
on the standard, in order to be able to introduce a correction 
whenever accuracy of measurement should permit and circum- 
stances necessitate it. 

This requirement for a standard necessarily entails on the 
one hand a knowledge of the relations Avhich exist between 
the standard and the causes of its variation, and on the other 
hand the possibility of an accurate and independent measure- 
ment of these causes. 

Further, having no constant standard, it is impossible to 
produce two quantities of the same kind bearing a fixed 
and known ratio to each other ; consequently no idea can be 
formed of the accuracy of the test-method adopted ; and if such 
is impossible, we are also unable to improve the test-method in 
itself, i. e. with respect both to accuracy and sensitiveness. 

The inconstancy of a standard acts therefore perniciously 
in two directions : it prevents us from being able to execute 
accurate measurements even with the most accurate and sen- 
sitive test-methods, supposing such are available, and, further, 
leaves us in the deplorable condition of not being able to 
improve the test-method although we may be convinced that 
the method of testing requires such improvement. 

It may be safely asserted that in any of the branches of the 
physical sciences where constant standards do not exist the 
])rogress in accurate knowledge of nature must be slow, if not 

This train of thought will, I think, invariably beset the 

physicist who endeavours to make photometric measurements. 

llecent experiments on the value of the electric light as 

compared with the ordinary means of illumination f called my 

attention forcibly to this point. 

* From the Jovirnal of the Asiatic Society of Bengal, vol. xlviii. part 
ii. 1879. Communicatfd by the Autlior. 

t These experiments I had to institute on behalf of the Board of Di- 
rectors of the East-Indian IJailway Company, under orders of the Secre- 
tary of State for India to inquire into the feasibility and practicability of 
lighting up Indian Railway-stations by the electric light. 

On a neio Standard of Light. 393 

Old Standards for Light-measurements. — Up to the present 
in England the Standard Candle * has been adopted as the 
standard of light, the unit of light being defined as that light 
■which the said candle emits when burning steadily at a certain 
definite rate. In France the Carcel Burner (bee Carcel) has 
been introduced as the standard of light, the unit of light in 
this case beino; defined as that light which emanates from a 
good moderator lamp burning pure colza oil at a given definite 
rate. The ratio of these two arbitrary units is given by 
several authorities very difl:erently, the mean value being 

10 standard candles = 1 Carcel burner. 

These two standards of light, although answering perhaps 
certain practical requirements, are by their nature ill-adapted 
to form the units of light-intensities. A good and trustworthy 
standard should possess absolute constancy, or, if not, should 
afford the possibility of application of a correction for the 
variation, and moreover should be capable of accurate repro- 
duction. These qualifications are certainly not possessed by 
the standards at present in use. 

A candle of whatever compound and size will partake of 
something of the nature of a complex body, an accurate re- 
production of which must always be a matter of great diffi- 
culty. Exactly the same holds good for the Carcel burner. 

Further, the amount of light these standards produce de- 
pends to a very considerable extent on external influences, 
which do not allow of easy control or measurement, and which 
therefore cause variations in the standard light for which it 
becomes impossible to introduce a correction. For instance, 
the rate and regularity with which a candle burns and the 
amount of light it gives depend, in addition to the material of 
which the candle consists, on the ready and regular access of 
oxygen. In a closed-up place, like the box of a photometer, 
if the draught is not well regulated or the supply of fresh air 
not quite constant, it can be easily observed that the very 
same candle may emit light at different times varying as much 
as 50 per cent. Another difficulty is introduced by the varia- 
tion of the length of the wick, and of the candle itself, by 
which the standard light necessarily alters its position in the 

* The Meti-opolitan Gas Act, 1860 (23 and 24 Vict. cap. 125, sect, xxv.) 
defines the standard candle as : — " Sperm candles of 6 to the pound, each 
burning 120 gi-ains an hour." I have tried the standard candles as made 
by two different manufacturers, Messrs. Field and Co. and Mr. Sugg. 
These candles are sold as six to the pound, and consume, according to my 
own experiments, about 8-26 grams per hour when placed in a large room 
and direct di'aughts excluded. 


394 Mr. L. Schwendlcr m a 

photometer, and consequently its quantitative effect on a given 
point. These difficulties might be overcome to a certain ex- 
tent by mechanical means — as, for instance, by cutting the 
wick automatically within equal and short intervals of time, 
and by })lacing the candle in a closely fitting metal tube, 
against the top rim of which a spring presses the burning 
candle — in fact, a similar construction to that used for carriage- 
candles. But, to say the least, all such arrangements are 
cumbersome. Without going into further details with refe- 
rence to the Carcel burner, it may be said that the disadvan- 
tages of this standard are at least equally great. In fact it 
appeared to me that the production of a standard light by 
combustion is not the right method ; the flame resembles too 
much organic life with its complex and incessantly varj'ing 
nature. Gauging mechanical force by the power a particular 
horse of a certain breed is able to exert, can scarcely be called 
a less scientific standard than the combustion standard for 
measuring light. Under these circumstances I thought it 
best to leave the old track, and produce the standard of light 
bi/ the heating effect a constant current has in passing through 
a conchictor of given mass and dimcjisions* . 

JS^eio Standard of Light. — Several platinum photometric 
standards were made and tried. If the current passing through 
the platinum was kept constant, the light produced was also 
constant; and for the same current and the same platinum 
standard the light was always of the same intensity, under 
whatever other circumstances the experiments were con- 

Platinum e\-idently is the best metal which can be chosen ; 
for it does not change in contact with oxygen, it can be pro- 
cured very pure, and its melting-point is high enough to allow 
an intense light. 

It is probable that at a high temperature platinum becomes 
volatilized ; but this process can only be exceedingly slow, and 

* The idea of using the light produced by a conductor through which 
a strong cuiTent passes as the unit of light appeared to me so uatui-al and 
simple, that I could scarcely understand why it had not been proposed 
and acted upon before. 

I could, however, find nothing on the subject anywhere, xmtil lately 
my attention was called to a small pamphlet written by Zcilluer in 185l>, 
in which the same idea occurs. In the preface to his Inaugural Disserta- 
tion, Zollner says : — " Andererseits aber auch zu zeigen, dass ein galvanisch 
g-liihendcr Platindraht von den bis jetzt bekanuten Lichtquellen zur Auf- 
stellung einer photometrischen Einheit, trotz mancher practischer Schwie- 
riglceiten, ^-ielleicht dcnnoch das geeignetsto Mittel sei." 

I have since loanit that Dr. Draper, as early as 1844, proposed a " unit 
lamp " consisting of a platinum strip heated by an electric cuiTeut. 

new Standard of Light. 395 

therefore the light produced by a standard cannot alter per- 
ceptibly in time. / To make the light constant from the moment 
the current passes, i. e. to establish dynamic equilibrium be- 
tween the heat produced and the heat lost per unit of time, it 
is necessary to make the arrangement in such a manner that 
the electric resistance offered by the standard is only in the 
piece of platinum intended to be made hot by the current, and 
not in the other parts of the circuit. 

For this reason I find it best to cut the piece of platinum 
out of a platinum sheet. 

Figure 7, Plato XI. gives the form in actual size. The two 
ears, left white in the drawing, may then conveniently form 
the electrodes between the leading wires and the piece of 
U-shaped platinum which has to produce the light. As the 
U-shaped portion is left in its natural connexion with the ears, 
the contact takes place over a large surface ; and therefore the 
contact resistance must be small. This special form, if the 
dimensions are defined as well as the weight of the platinum 
sheet out of which it is cut, can be easily reproduced any- 
where. Further, it is required to exclude the draught from 
the heated platinum. This is best done by putting on a cover 
of thin white glass. One half of it is left white ; the other half 
is blackened on the inside. This precaution is required in 
order to ensure that light emanating from one side only of the 
platinum is used in the photometer ; otherwise light from the 
back part of the heated platinum would be reflected into the 
photometer. This part is unknown, and therefore could not 
be taken into account when measuring the light emanating 
from one side of another light. In fact, to be able to form 
right conclusions from photometric measurements, it is neces- 
sary to arrange the experiment in such a manner that either 
the two lights under comparison throw the same fraction of 
the total light into the photometer, or, if this is impossible, to 
ascertain this proportion accurately. 

The platinum light-standard (P. L. S.), described before, we 
will call in future A. Sending a current of 6*15 webers 
through it (15° deflection on my large tangent galvanometer, 
for which the constant =2-296 C. G. S.), the P. L. S. (A) 
produces a light equal to 0-69 Sugg's candle, or, 

1 Sugg's candle=l-44 P. L. S. (A) with 
6*15 webers. 

Hence, if this particular light were adopted as the unit, we 
might define it as follow^s : — 

6*15 webers passing through a piece of platinum 2 millims. 
broad, 36*28 millims. long and 0'017 millim. thick, weighing 


Mr. L. Schwendler o?i a 

0-0264 grm., having a calculated resistance =0-109 S. U. and 
a measured resistance =0-143 S. U. at 00° F., gives tlie unit 
for light-intensity *• 

Photometric Measurements. — Havinfif now a constant light, 
it became possible to measure the variations of light which the 
combustion standards invariably show. 

For instance, one of Sugg's candles was compared with the 
P. L. S. (A) with the result shown in the following table : — 

Distance in millimetres. 


P. L. S. (A) 
with 6- 15 webers. 

Sugg's candle. 

These readings were taken k- 5^ 
in about five minutes. 8 B 


The P. L. S. (A) waa kept at the 
same position = 100 millims. 

Sugg's candle was moved in order to 
get the light equal. 

The variations observed were actually 
in the caudle and not in the pla- 
tinum standard, as the eye could 
easily discern. 

This gives as an average : — 

1 Sugg's candle = l-44 P. L. S. (A) with 6-15 webers. 

* In order to show that a platinum light-standard can easily be repro- 
duced, I will give here some actual measui-ements : — 

The platinum sheet out of which the P. L, S. (A) was cut weighed 
0"03G4 gram per square centimetre. From this the weight of the part 
which becomes hot, calculated, gives 0-0264 gi-am. The resistance of 
the standard, measured at 66° F,, gave 0*143 S. U., including contact 

Now another piece of platinum sheet 26x28 millims. was found to 
weight 0"265 gram. The piece cut oft' which actually becomes hot = 0*026 
gram, which agrees within 00004 gi-am with the weight found by calcu- 
lation for the P. L. S. (A) actually used. 

TaMng the specific resistance of mercury =961901 „iQori 

„ „ of platinum (annealed) = 9158 ( -' 

s. u. 
tlie calculated resistance of the platinum which becomes hot=0-109 ) at 

measured resistance, including contact resistance =0"14;J j 66°F.; 

or contact resistance probably =0-034 S. U. 

It is therefore much more accurate to define the P. L. S. by weight 
than by resistance. 

new Standard of Light. 397 

,■■. ' = , ,. , or total variation of the candle about 30 per 
Mm. 1-21' ^ 

cent, from the average in the very short interval of time of 

about five minutes. This needs no further comment. Some 

additional experiments were made in order to ascertain the 

variation of the light of a standard candle. 

The P. L. S. (B)* with a current=5*9 webers was used as 

1st candle, 7 readings in 10 minutes. 

Mean = 1-08 P. L. S. (B) ; 

— —=—-—-, or total variation=17*6 per cent, 
mm. I'OO '■ 

The maximum was obtained directly after having opened 
the photometer, when fresh air entered. 
27id candle, 10 readings in 14 minutes. 

Mean = 1-07 P. L. S. (B) ; 

— 7-^=K-7^, or total variation = 59 per cent, 
mm. O'bU 

The minimum was obtained directly after freshly lighting 
the candle. 

3rd candle, 12 readings in 24 minutes. 

Mean = 1-07 P. L. S. (B) ; 

'/ ' = ——-, or total variation =46 per cent, 
mm. 0"bl ^ 

The lowest reading was obtained shortly after lighting the 

Ath candle, 14 readings in 22 minutes. 

Mean = 0-94 P. L. S. (B) ; 

— r^=7T-=T^, or total variation = 72 per cent, 
mm. 0-0 8 ^ 

The lowest reading cannot be accounted for. 

Two new platinum light-standards, of the same form and 
size as the P. L. S. (A) described before, were placed in cir- 
cuit of eight Grovels cells connected up successively and "svith a 
mercury rheostat in circuit, to keep the needle of the 'tangent 
galvanometer at a constant deflexion. 

These two new P. L. S., called II. and III., were placed in 
the photometer to compare their lights and by it test the 

* This platinum standard (B) was tlie first made and has a different 
form from the other (A) described. Dimensions and weight cannot be 
accurately given now. 


Mr. L. Schwendler on a 

accuracy of the photometer-readings, and other influences to 
be named further on (see fig. 8). 

fZ + f/'=D = 250 millims. (constant). 

Light i produced by P. L. S. (III.) ; light i' produced by 
P. L. S. (II.), — tho balance between the two lights being ob- 
tained by moving the prisms mthin that fixed distance. A 
piece of red glass Avas used for taking the readings. 

In the following Table the results are given : — 

P. L. S. 


a 2 




.2 ** 


Remarks and Particulars. 


producing i' 

producing i 




d' millims. 

d millims. 


from prism. 

from prism. 






Both lights having glass 




covers ; but glasses were 




quite clear. 











A clear glass cover on No. 












III. ; no glass cover on 



No. II. 





A clear glass cover on No. 












II. ; no glass cover on 




No. m. 









A glass cover on No. III., 

• 98 











the back of it covered 




inside with black pajjer ; 




a clear glass cover on 



No. II. 







new Standard of Light. 
Table {continued^ 




. S. 

A *^" 


J % 


s a 


5 o 







Eemarks and Particulars. 


producing i' 

producing i 

"i w) 



d' millims. 

d millims. 

ca ^ 


from prism. 

from prism. 






Both lights covered up 




with glass covers, each 




glass cover having inside 



a black paper. 



Current increased by de- 












creasing the resistance of 




the mercury rheostat, but 




kept constant at 21°. 




Clear glass again on both, 



like experiment No. I. 
Clear glass cover on No. III. 












No glass cover on No. II. 











Clear glass cover on No. II. 












No glass cover on No. III. 













Both the clear glass covers 




















The deflection 18°'8 represents a current =7'82 webers. 
The deflection 21° represents a current =8'81 webers. 
From these results the follo^ving conclusions can be drawn: — 
The thin glass covers, as was to be expected, absorb a 

400 Mr. L. Schwendler on a 

measurable quantity of lifrlit. Compare the results of experi- 
ments 1, 2, and 3, and of G, 7, 8, and 9. 

Covering the glass covers inside with black paper to avoid 
back-reflection, appears to weaken the light, as was to be ex- 
pected. Compare the results of experiments 1, 4, and 5. 


The ratio - of the two lights is independent of the strength 

of the current, which it ought to be. 

These results, although showing nothing extraordinary, i. e. 
what could not have been foretold without making the experi- 
ments, are nevertheless valuable, since they prove, in the first 
place, that thin glass covers take away very little light, and 
that back-reflection is also very little ; but small as these in- 
fluences are, they have been unerringly measured by the pho- 
tometer, showing this instrument to be very accurate and the 
eye quite trustworthy. That the light i, produced by P. L. S. 
III., was so much more intense than i', produced by P. L. S. 
II., is due to the fact that the platinum sheet out of which 
no. II. was cut was much thicker than the other. 

Detailed Description of the Standard and the Method of using it. 

Fig. 9, Plate XI., gives the construction of the platinum 
standard in half its natural size. I need not give further ex- 
planation on this point, as every thing will be readily understood 
from the drawing. 

Fig. 10 shows the diagram of the connexions : — 

P. L. S. is the standard. 

G, a current-indicator, or, better, current-measurer. The 
deflecting-ring must consist of a few convolutions of thick 
copper wire, of no perceptible resistance. The small magnet 
needle is best pivoted, carrying a long aluminium index. 

B is the battery, consisting of a few elements of high E. M. F. 
and low internal resistance connected up successively. Grove's, 
Bunsen's or large Daniell's cells will answer well for the 

(1) is a stopper, by which the circuit can be conveniently 
opened or closed. 

M is a mercury rheostat of about one unit resistance. A 
groove of about 1 millim. section and 1 metre total length is 
cut in hard wood (not ebonite, as mercury does not run well 
in ebonite). The hard wooden board is supported by three 

Further, the mercury is in perfect metallic contact with two 
iron terminals,//. These terminals are not to be fixed to the 
board. They are simply placed in the mercury, which fills 
small reservoirs at each end of the mercury thread. 

new Standard of Liglit. 401 

The resistance of the mercury rheostat can be easily altered 
by moving the bridge h along the two parallel mercury-grooves. 
If the bridge is taken out, the total resistance of the rheostat 
is in circuit. 

If the bridge h is close to the two terminals//, the resist- 
ance of the rheostat is nil. 

This range of resistance with about 6 to 10 volts will prove 
sufficient to make the current strong enough and to keep it 
constant for many hours, especially if the precaution be taken 
to open the circuit when no light is required. The bridge h 
consists of a strip of copper at least 2 centims. broad and 1 
millim. thick. The knife-edges which dip into the mercury 
are amalgamated. 

The current-measurer G has been gauged by comparison 
with a standard tangent-galvanometer ; so that the currents 
indicated by certain deflections of the needle are correctly 
known in absolute measure. 

Whenever a photometric measurement is made, the current 
is adjusted to its defined strength ; i. e. the given known de- 
flection is procured by moving the copper bridge b. 

If the instrument Gr is well constructed, this adjustment of 
current-strength can be executed as accurately as weight- 
measurernent by a chemical balance. 

Correction for the Standard. 

Although with the above arrangement it will be always 
possible to keep the current constant and up to its defined 
amount, it might nevertheless happen under particular cir- 
cumstances that the current producing the light has been 
rendered different from the current for which the standard has 
been defined. 

In this case the following correction can be applied : — 


where c is the current for which the intensity of the light has 
been defined as unity, 7 the actually observed current, and a 
the coeflficient for platinum which gives the percentage varia- 
tion of ^ resistance at high temperature, 1500°-2000° F. for 
1° Celsius. 

This correction has been developed on the supposition 
that the light produced in the given piece of platinum is pro- 
portional to the work done by the current through the resist- 
ance of the platinum, and further, that, temperature and light 

402 On a neio Standard of Light. 

arc ]iroportional. These suppositions are almost correct for 
small variations of the current. 

In conclusion it may bo stated that it was ascertained that 
the platinum light-standard (B) produced the unit intensity 
of light (the unit of light equal to the light emitted by tho 
standard candle) at a total expenditure of energy equal to 427 
li ergs per second. Of these, 300 H ergs -svere actually trans- 
formed into light by heating the platinum up to a high tem- 
perature ; while the remaining 127 O ergs were lost for 
illuminating-purposes, being used for raising the temperature 
of the circuit exclusive of the platinum standard. 

The platinum light-standard (A) being made of much 
thicker platinum sheet, showed a much less favourable result. 
The unit of light by (A) was produced at a total expenditure 
of energy equal to 122() H ergs per second, of which 725 D, 
ergs were actually transformed into light ; the remaining 501 
£l ergs were wasted in heating the circuit to low temperature 
(no light). Considering that the unit of light can be pro- 
duced in an electric arc at a total expenditure of energy of 10 
n ergs per second only (see my ' Precis of Heport on Electric- 
Light Experiments,' London, 1st Nov. 1878, p. 11), when 
produced by Siemens's intermediate dynamo-electric machine, 
it follows that, from an engineering point of view, light by 
incandescence can scarcely be expected to compete with light 
by disintegration (electric arc). 

Li fact, it appears that light h\ incandescence \^ &c^Tce\y oxxj 
cheaper than light by combustion. The reason for this is that 
the temperature of an incandescent platinum wire is not very 
much higher than the temperature of a flame, and that for unit 
volume the mass which has to be kept heated in a piece of 
platinum is much larger than the mass in a flame. Unless we 
should be fortunate enough to discover a conductor of electri- 
city with a much higher melting-point than platinum, and 
that the specific Aveight and specific heat of that conductor is 
also much lower than for platinum, and that at the same time 
the new conductor does not combine at high temperatures 
with oxygen, we can scarcely expect that the principle of in- 
candescence will be made use of for practical illumination. 

Further, itwas ascertained that the resistances of the platinum 
light-standards (not including contact resistance) were as 
follows : — 

P. L. S. (B) = 0-136 ohm at 22°-2 C. 

= 0*876 „ at the temperature of the standard 

f\.Q'7 f 

where the light was measured, or increase ,, ■,..,. = 6"44. 

Lord Eayleigh's Investigations in Optics. 403 

P. L. S. (A) = 0-102 olim at 18°-9 C. 

= 0*964 „ at the temperature of the standard 

where the light was produced, or increase ^ -. .^ = 9'45. 

I regret that I have not been able to calculate from the 
above results the temperature of the heated platinum, since I 
could not procure in time a copy of Dr. William Siemens's 
Bakerian Lecture (1871), which at present, to my knowledge, 
is the only source whence the increase of resistance of platinum 
at high temperatures can be found. 

To sum up, the advantages of the new standard of light are: — 
The light is perfectly constant if the current be kept constant ; 
it allows a correction to be made for the variation of the current 
if this variation is known ; it can be reproduced accurately 
everywhere if ordinary precautions be taken to secure pure 
platinum * ; its magnitude can be altered to any extent to suit 
certain practical purposes by simply varying the elements of 
weight, shape, and size of the platinum, or the strength of the 
current passing through it ; it does not alter of itself either in 
intensity, size, or position, and therefore by it most accurate 
photometric measurements can be executed ; the standard can 
be easily made to fit into any adopted system of absolute units. 
Hence the new standard fulfils all the recognized conditions 
of a perfect and rational standard ; and therefore it would be 
advisable to adopt it in future as the practical standard for 
light-measurement. There would be no practical difficulties 
met with in the introduction of the new standard for technical 

XLYI. Investigations in Optics, zoith special reference to the 
Spectroscope. By Lord Eayleigh, F.R.S. 

[Continued from p, 274.] 

§ 4. Influence of Aberration. 

IN the investigations of § 2 the wave-surface was considered 
to be plane, or (after passing through a condensing lens) 
spherical. As all optical instniments are liable to aberration, it is 
important to inquire what effects are produced thereby upon the 

* The coniluctivity of any metal is much lowered by slight impurities ; 
and platinum does not form an exception ; hence great care must be exer- 
cised in the selection of platinum for the light-standard. Dr. William 
Siemens, in his Bakerian Lectm-e says : — " The abnormal resistance of 
some platinum is due chiefly to the admixtm-e of iridium or other metals 
of the same group ; and it appears that platinum prepared by the old 
welding process is purer, and therefore better suited for electi-ical purposes, 
than the metal consolidated by fusion in a Deville fui-nace." 

404 Lord Rayleigh's Investigations in Optics. 

intensity-curves, and especially to ascertain at what point a 
sensible deterioration of definition ensues. Tlie only work 
bearin<Tj upon the present subject with which I am acquainted 
is Sir G. Airy's investigation " of the intensity of light in the 
neighbourhood of a caustic"* ; but the problem considered by 
him relates to an nnlhnited beam. 

Considering in the first place the case of a beam of rectan- 
gular section, let us suppose that the aberration, or error of 
phase, is the same in all Acrtical lines, so that the actual wave- 
surface is cylindrical. With origin at the centre and axis of 
X horizontal, the aberration may be expressed in the form 

cx^-\-fx^ + (1) 

No terms appear in x or a?: the first would be equivalent to a 
general turning of the beam ; and the second would imply im- 
perfect focusing of the central parts. In many cases the cir- 
cumstances are sj'mmetrical with respect to the centre ; and 
then the first term which occurs is that containing .r*. But 
in general, since the whole error of linear retardation which 
we shall contemplate is exceedingly small in comparison with 
other linear magnitudes concerned in the problem, the term 
in x^ is by far the more important, and those that follow may 
be neglected. 

As in the case of no aberration (treated in § 2), the distribu- 
tion of brightness in the image of a point is similar along every 
vertical line in the focal plane ; and therefore the image of a 
vertical line follows the same law of brightness as applies in 
the case of a point to positions situated along the axis of ^. 
The phase of the resultant at any point | is by symmetry ihe 
same as that of the secondar^^ wave issuing from the centre 
(a;= 0) ; and thus the amplitude of the resultant is proportional to 

y'\o&2'7r{^-^cx^^dx (2) 

In Sir G. Airy's problem the upper limit of the integral (2) 
is infinite. Fortunately for my purpose the method of calcu- 
lation employed by him is that of quadratures, and the inter- 
mediate results are recorded (p. 402) in sufficient detail. In 
order to bring (2) into conformity with Airy's notation, we 
must take 

27rc^' = ^7r«i>^, -—^ — —m^w; ... (3) 
- V ^ 

we thus obtain 


cos i7r(a)' — 7na))cfG>, . . . (4) 



Cambridge Phil. Trans, vol. vi. 1838. 

Lord Rajleigh's Investigations in Optics. 


in which the upper limit of the integral is the cube root of the 
extreme aberration expressed in quarter-periods. For example, 
the upper limit is unity when the phase at one extremity is a 
quarter-period in advance, and that at the other extremity a 
quarter-period in the rear, of the phase at the centre. 

The influence of aberration may be considered in two ways. 
We may suppose the aperture {a) constant, and inquire into 
the effect of an increasing aberration (c) ; or we may take a 
given value of c (?'. e. a given wave-surface), and examine the 
effect of a var^-ing aperture. To the latter comparison Airv's 
results are more immediately applicable. The following Table, 
easily derived from that given by him, exhibits the values of 
cos^7r(a)^ — ??i&))(/(w, between the limits specified in the head- 
ings of columns 2, 3, 4, 5. The results are applicable at once 
to the comparison of the amplitude-curves corresponding to 
Aarious apertures, since the relation of m to f in (3) is inde- 
pendent of a. To obtain intensities, it would be necessary to 
square the numbers given in the Table. 


Value of m. 

From to 

From to 

From to 

From to 


+ 0929 







+ •0197 



+ 0343 

+ •0142 











+ •0018 








+ 0411 


































+ 1-2 





+ 1-6 











+ 0303 



+ •1172 





















The second column relates to the case where the aperture is 
such that the aberration between the extremities and the centre 
is one quarter of a period, or (which is the same thing) where 
the wave-surface at the extremities deviates by a quarter wave- 
length from the tangent plane at the central line of inflection. It 
'W'ill be seen that the position of maximum illumination deviates 
sensibly from the centre (m = 0, |=0). This is no more than 
might have been expected, since the plane which most nearly 
coincides with the actual wave-surface is inclined to the cen- 

FJiil Mag. S. 5. Vol. 8. No. 50. Nov. 1879. 2E 

406 Lord Rayleigh's Investigations in Optics. 

tral tangent plane. The third column relates to an aperture 
about a fourth part larger, for which the extreme aberration 
is (1*26)^ quarter-periods or nearly half a period, and the 
fourth colunm relates to an aperture such that extreme aber- 
ration amounts to about three quarters of a period. 

From columns 2 and 3 we see that an increase of aperture 
up to that corresponding to an extreme aberration of half a 
period has no ill effect upon the central band, but it increases 
unduly the intensity of the tirst lateral band at m=+^'2. 
Indeed the principal objection to much greater apertures is 
this augmented importance of the lateral band. The practical 
conclusion is that the best results will be obtained with an 
aperture giving an extreme aberration of from a quarter to 
half a period, and that with an increased aperture aberration 
is not so much a direct cause of deterioration as an obstacle to 
the attainment of that improved definition which should accom- 
pany the increase of aperture. 

We will now suppose the aperture given, and examine the 
effect of increasing aberration. In applying the tabular results 
we must have regard to the factor (4e)-^, which occurs in (4), 
and we nmst take account of the variation of the relative scale 
of m and ^ in passing from one curve to another (^ QC?n \/4:c). 
The results for three cases are expressed graphically by the 
curves in fig. 6. The first, which rises highest, represents 

Fio-. G. 

the intensity at the various points of the focal plane when 
there is no aberration — the same as in fig. 1. The second and 
third curves represent the intensities when the extreme aber- 
i-ations are a quarter period and half a period respectively. 
The total areas of these curves are the same, since the whole 

Lord Rayleigh's Investigations in Optics. 407 

quantity of light in the beam is independent of the aberration; 
and this area is equal to that of a rectangle whose height is 
the maximum ordinate A of the first curve, and width the 
distance B between and the first position of zero intensity. 
It appears that aberration begins to be distinctly mischievous 
when it amounts to about a quarter-period, i. e. when the 
wave-surface deviates at each end by a quarter wave-length 
from the true plane. The most marked effect is the increased 
importance of the lateral band on one side, and the approxi- 
mate obliteration of the lateral band on the other side. 

When the aberration is symmetrical about the centre of 
the beam, the term in x^ vanishes, and the whole effect is of 
higher order. In general the term in x^ will preponderate ; 
and thus the problem for a symmetrical beam resolves itself 
into the investigation of aberration varying as x^. In one 
respect the problem is simpler than the preceding, on account 
of the symmetry of the intensity-curves ; but in another it is 
more complicated, since the phase of the resultant does not 
correspond with that of the central element. The intensity is 
represented by 

+ [r"sin2,r(i|+yi-«)rf.,T, .... (5) 

and requires for its calculation two integrations. These could 
be effected by quadratures ; but the results would perhaps 
scarcely repay the labour, especially as the practical question 
differs somewhat from that here proposed. The intensity- 
curve derived from (5) represents the actual state of things on 
the supposition that the focusing adopted is that proper to a 
very small aperture ; whereas in practice the aberration would 
be in some degree compensated for by a change of focus, as 
it is obvious that the real wave-surface, being curved only in 
one direction, could be more accurately identified with a sphere 
than with a plane. 

Some idea of the effect of aberration may be obtained from 
a calculation of the intensity at the central point (|=0), 
where it reaches a maximum ; and this can be effected with- 
out quadratures by the aid of a series. In this case we have 
instead of (5 ), 

4 r ( '"cos {^'7rfx')dx\ " + 4 r f'^sin {2'Trfx'')dx\ . . (6) 

Now by integration by parts it can be proved that 


408 Lord Rajleigh's Investiyations in Optics. 

whence by separation of real and imaginary parts, and putting 
X equal to unity, 

J;cos(..^y.=cos. [l-^^i)%^^Jigl^_...j 

5 5.9.13 ' 

coc/:P ^^^'^' I W 1 r8^ 

^^'''\5 5.9.13 +'7- ^^^ 

Calculating from these series I find 

f ri 4x^ 1'3G704 f' . ,, ,., -21352 
I cos(i7r.f*V.r= — — — , ) sm(i7r.r^)^^= , 

Jo V-^ c'o v^ 

[ I 'cos (i 17x^)^1 A " + r r 'sin (i 7ru.-*)f/.r] " = -9576. 

1 'cos {^'Trx^)cl.v= -87704, j 'sin (^7r.r^)^/.r= -26812, 

Jo » 

r I 'cos {^'irx^)±^ ' + [ j 'sin (i7r.r*)(f J ^= '84109. 


j cos (7r.r*)c?.r=-64357, j sin (7r.2;*)(/.i'= "33363, 
Jq «- 

r| \os (Trx'^)dx\ + ri 'sin(7r^*)di1 =-52549. 

Thus an extreme aberration of one eighth of a period reduces 
the intensity at the central point from unity, corresponding to 
no aberration, to '9576. With an aberration of one quarter of 
a period the intensity is -84109 ; and with an aberration of half 
a period the intensity is reduced to -52549. We must remem- 
ber, however, that these numbers will be sensibly raised if a 
readjustment of focus be admitted. 

In most optical instruments other than spectroscopes the 
section of the beam is circular, and there is symmetry about 
an axis. The calculation of the intensity-curves as affected 
by aberration could be performed by quadratures from tables 
of Bessel's functions ;but, as in the case last considered, the 
results are liable to a modification in practice from readjust- 
ment of focus. For the central point avo may obtain what we 
require fiiom a series. 

Lord Rayleigh's Investigations in Optics. 409 

The intensity may be represented by 

[2 Tcos {hr'')rdry+ [2 jsiu {hr^)rdry, 

*/'0 •-0 

the scale being such that the intensity is unity in the case of 
no aberration (/i = 0). As before, we find 



h L 

2J cos(A/) .c^.^cosA |1- |^+ 6, 10./^, 18 - • j 

Thus, when A = ^ tt, 

.f' ,, ,, , 1-32945 ^C' . ^, ,, - -35424 
Jo v^ Jo '^•^ 

[2 rcos(i7r/) /•(7y]2+ [2 Tsin (Itt;-*) r (f;-]2 = -9464. 

Jo Jo 

Again, when h = ^'7r, 

2 j cos (h'TTi'^) r f/;' = -77989, 2 Tsin {iTrr^} r(/r= -43828, 
[2 j cos (i7r/'^)rf/7-]2 + [2 f'sin (^Trr*) 7'(;r]2=-8003. 

Jo n 

Again, when h — Tr, 

2 1 'cos (tt?-*) ;• fZ?-= -3740, 2 j sin (tt;'") r (fr= -5048, 
Jo Jo 

[2 rcos(7r?'*) rdvJ+[_2 Tsin (tt;-^) r rf;']2 = -3947. 

Jo Jo 

Hence in this case, as in the preceding, we may consider that 
aberration begins to be decidedly prejudicial when the wave- 
surface deviates from its proper place by about a quarter of a 

As an application of this result, let us investigate what 
amount of temperature-disturbance in the tube of a telescope 
may be expected to impair definition. According to the ex- 
periments of Biot and Arago, the refractive index /x for air at 

410 Lord Rayleigh's Investigations in Optics. 

temperature t° C. and at atmospheric pressure is given by 

/A— 1 = 

If we take the freezing-point as standard temperature, 

Zfi=-l-ltx\0-^ (11) 

Thus, supposing that the irregularity of temperature t extends 
through a longth /, and produces a retardation of a quarter of 
a wave-length, 

or, if we take \=5'3 x 10~*, 

lt = U, . (12) 

the unit of length being the centimetre. 

We may infer that, in the case of a telescope-tube 12 centi- 
metres long, a stratum of air heated one degree Cent., lying 
along the top of the tube and occupying a moderate fraction 
of the whole volume, would produce a not insensible eft'ect. 
If the change of temperature progressed uniformly from one 
side of the tube to the other, the result would be a lateral dis- 
placement of the image without loss of definition; but in 
general both effects would be observ^able. In longer tubes a 
similar disturbance would be caused by a proportionally less 
difference of temperature. 

In the ordinary investigations of the aberration of optical 
instruments attention is usually given to a quantity called the 
longitudinal aberration, which is the distance between the geo- 
metrical focus and the point at which the extreme ray meets 
the axis. In order to adapt these calculations to our purpose, 
it is necessary to establish the connexion between longitudinal 
aberration and the deviation of the actual surface of the con- 
verging waves from a truly spherical surface having its centre 
at the geometrical focus. 

If the axis of symmetry be taken as that of r, and the tan- 
gent plane to the wave-surface as plane of xg, we have as the 
equation of the ideal wave-surface, 

{z-ff + a^'^^y'^^f, 

f being the distance of the focus from the origin ; or if we 
limit our attention to the plane g = 0, 

The actual wave-surface, having at the origin the same cur- 
vature, is represented by 

^'=^7+^3, (14) 

where k is a constant depending upon the amount of abcr- 

Lord Rtiyleigh's Investiyations in Option. 411 

ration. The distance (A) between the surfaces is given by 

h = ,-,' = {l-^^ (15) 

The equation to the normal to (12) at the point c', x is 

— 1 x 4kx^ ' 

so that when f =0, 

1+ —^ ^ 

If the longitudinal aberration be called hf, 

hf=K-f=hj{'^-^x) (16) 

Thus by (13) and (14), 

1 2 


5/- 4/2 "4-; (17) 

where « denotes the angular semi-aperture. Taking the 
greatest admissible value of h as equal to \ \, we shall see that 
8/ must not exceed the value given by 

8/=X«-2 (18) 

As a practical example, we may take the case of a single 
lens of glass collecting parallel rays to a focus. With the 
most favourable curvatures the longitudinal aberration is about 
fa^; so that a* must not exceed X-r-/. For a lens of 3 feet 
focus, this condition is satisfied if the aperture do not exceed 
2 inches. In spectroscopic work the chromatic aberration of 
single lenses does not come into play, and there is nothing to 
forbid their employment if the above-mentioned restriction be 
observed. I have been in the habit of using a plano-convex 
lens of plate-glass, the curved side being turned towards the 
parallel light, and have found its performance quite satisfac- 
tory. The fact that with a given focal length ihe extreme 
error of phase varies as the fourth power of the aperture is 
quite in accordance with practical experience ; for it is well 
known that the difficulty of making object-glasses for tele- 
scopes increases very rapidly with the angular aperture. 

When parallel rays fall directly upon a spherical mirror, 
the longitudinal aberration is only one eighth as great as for 
the most favourably shaped lens of equal focal length and 
aperture. Hence a spherical mirror of 3 feet focus might have 
an aperture of 2^ inches, and the image would not suffer ma- 
terially from aberration. 

[To be continued.] 

{ 412 ] 

XLVII. On the Conjugate Pontions of two Circular Coils 
of Wire. By W. Grant, Assistant in tlie Physical Labo- 
ratory , University College, London* . 
[Plate XII.] 

WHILE recently engaged on some experiments on in- 
duction, I observed certain circumstances which I 
had not before noticed, and which seemed deserving of further 
attention. I was therefore led to inquire a little more closely 
into these matters ; and although the investigation is by no 
means full or complete, I have obtained one or two results 
which I thought I might venture to lay before the Physical 
Society. The apparatus used in these experiments consisted, 
as at first arranged, of two coils of copper wire, one of which 
was connected in circuit with a battery of three Leclanchp 
cells, and with a microphone which was actuated by a watch, 
while the other was connected with a telephone, in order that 
the induced currents, while passing through it, might render 
audible the beating of the watch which was used as the source 
of sound. 

A modification of this arrangement was afterwards tried, 
a Grove's battery of twelve cells being substituted for the 
Leclanche battery, and a key being used for making and 
breaking the circuit. This was done in order to obtain 
greater inductive effects between the coils than could be ob- 
tained from the variations in the strength of the current which 
were caused by the action of the microphone. It was found, 
however, that with a little care in the adjustment of the coils, 
one cell gave sensibly as great an effect in the telephone as 
twelve cells ; in subsequent experiments, therefore, the Grove's 
battery was discarded, and that of Leclanche again re- 
sorted to. 

Now if two similar coils, connected as above described, 
are arranged with their planes parallel and their axes coin- 
cident, it is found that the}^ may be separated to a considerable 
distance before the sounds which are heard in the telephone on 
making and breaking the circuit are obliterated. But it is 
also found that if the planes of the coils are kept parallel, the 
one in connexion with the telephone (that is, the secondary 
coil) may be placed in certain positions in the neighbourhood 
of the primary coil, and even in contact with it, without 
sounds being heard in the telephone. This happens when 
the mutual inductive effect between the two coils becomes 
zero; ajid when they are so placed as to fulfil this condition, 
tehy are said to occupy conjugate positions relatively to each 

* Commuuicated bv the Physical Society, haviner been read Juue 28th, 
1879. ... 

PM.Mag. S.5.V0I.8.PI.XQ:. 







I I 




Oil the Conjugate Positions of two Circular Coils of Wire. 413 

With the first arrangement of apparatus it was possible to 
place the coils so as to get complete silence in the telephone. 
With the powerful current from twelve G-rove's cells and the 
key for making and breaking the f ircuit, however, the silence 
is not absolute ; but in the positions Avhich give a minimum 
of sound the sound is very faint, being just audible and no 
more. This faint sound may perhaps be accounted for partly 
because the different convolutions of wire in the secondary 
coil experience slightly different inductive effects from the pri- 
mary one, and partly because it is difBcult to adjust the posi- 
tions of the coils with any great degree of accuracy without 
having special arrangements for the purpose. 

Now it w^as found that the various conjugate positions in 
which the secondary coil could be placed in the neighbourhood 
of the primary one were situated in a path along which it 
could be moved either towards or away from the primary 
coil without sounds being heard in the telephone, but that 
with a slight deviation from this path to either side the sounds 
Avere again heard. 

In order to ascertain whether the direction of the currents 
in the secondary circuit was reversed when the coil was 
moved from one side of the path to the other, a delicate re- 
flecting galvanometer was substituted for the telephone, and 
the position of the coil so adjusted that on making and break- 
ing; the circuit no deflection of the galvanometer was observed. 
The coil was now moved sHghtiy away from this position, say, 
towards the right ; and the direction of the deflection of the 
galvanometer on making contact was noted, that on breaking 
being, of course, in the opposite direction. The coil was now 
moved towards the left to the other side of the path, and 
the direction of the deflections again observed ; and it was 
found that they were now reversed. We may therefore infer 
that this path (which, if it could be fully traced, would of 
course constitute a surface of revolution about the axis of the 
primary coil) divides space into two regions, in one of which 
the inductive action of the primary coil has the opposite di- 
rection to what it has in the other. 

This path appeared to be slightly curved ; and it seemed as 
if a part of it might very readily be traced. The part which 
appeared to be best suited for this pui-pose was that along 
which the secondary coil has to pass while being moved away 
from contact with the primary one parallel to it to a position 
at some distance from it, as here the inductive effect is 
greatest, and therefore any deviation of the coil from the 
proper position in the path is most easily detected. As the 
coils are further separated, however, the position of the path 
becomes more difficult to trace, until at last we lose it 

41 1 

Mr. W. Grant on the Conjugate Positions 

In order, then, to trace a curve wliicli would represent this 
path, it was necessary to find several points in it whose posi- 
tions could afterwards be accurately laid down. This was 
done by fixing the secondary coil in several positions succes- 
sively and determinincr the position of a certain point in it 
with relation to certain fixed objects, by measurements which 
were afterwards used as abscissjB and ordinates in tracing the 
curve. These measurements were taken in inches ; and their 
values are given in the annexed Table, where the columns 
headed x and y are those of abscissae and ordinates respec- 




















9 37 










6-44 ! 







No special arrangement was used to adjust the parallelism 
of the coils, and only one measurement was taken for each 
number ; hence the irregularity in the increase of the ordi- 
nates. The point whose position was determined in each case 
was the centre of the plane of the secondary coil ; and that is 
the point which is situated in the curve when silence is main- 
tained in the telephone. 

The curve (PI. XII.) is that found in this way ; and it repre- 
sents the path which the selected point of the coil has to follow 
in oi'der that silence may be maintained in the telephone. Ci 
and Cg are sections of the primary and secondary coils respec- 
tively ; C'2 and €''2 represent the secondary coil in two other 
conjugate positions. The lines A, A and P, P represent the 
axis and plane of the primary coil. The points a, h, c, &c. 
are the intersections of the abscissa} and ordinates, and repre- 
sent the successive positions occupied by the selected point of 
the secondary coil when the measurements were taken by 
means of which the curve was traced. As the coils became 
further separated, however, the position of the curve beciime 
less distinct ; and so no attempt was made to trace it further. 

If, now, we suppose the curve to rotate round the axis of 
the primary coil, a surface will be generated of which it is a 
section ; and if we observe the conditions necessary for placing 
the secondary coil in the curve in the proper position for 
silence, we may place it in any part of the surface with a like 

The reason whv we are enabled to trace a curve in this way 

of two Circular Coils of Wire. 415 

will be found by referring to the lines of force due to a cir- 
cular current. These lines are represented by closed curves 
surrounding the section of the wire through which the current 
floMs ; and they are given in Prof. Clerk Maxwell's work ' On 
Electricity and Magnetism/ vol. ii. pi. 18. If we draw tan- 
gents to them parallel to the plane of the circular current, it 
will be found that the points where they touch are situated in 
a curve somewhat similar to that which we have found by ex- 
periment. The two curves, however, will not be found to 
coincide exactly, except in the case where the secondary coil 
does not enclose a space — that is to say, when its diameter is 
infinitely small. With respect- to the curve dra^^^l thi-ough 
the points of contact of the tangents to the lines of force, it 
will be seen that the direction of all these lines between the 
curve and the axis of the circular current is away from, and 
that their direction on the other side of the curve is towards 
the plane of the circular current : hence on opposite sides of 
the curve their tendency is to produce currents in opposite 

If the curve is now supposed to revolve round the axis of 
the circular current, all lines of force enclosed by the surface 
generated will tend to produce currents in one direction, 
while all lines outside the surface will tend to produce currents 
in the opposite direction. Therefore, when the secondary^ coil 
is so situated with respect to this surface that as many lines 
of force pass through it in one direction as in the other, the 
resultant inductive eflect on it will be zero ; and this will be 
the case when it occupies any of the conjugate positions*. 

It is evident from this, therefore, that we may combine the 
coils in several ways for the suppression of inductive efl:ects : — 
first, by placing them close together face to face with their 
axes coincident, and so arranged that one of them may be 
moved across the face of the other parallel to their planes till 
a balance is obtained ; secondly, by placing them at some dis- 
tance apart with their planes parallel and their axes coincident, 
and so arranged that if their planes are vertical each of them 
may be made to rotate round its vertical diameter : then if 
they are joined together when their axes are coincident, and 
combined like parallel rulers, they may be made to rotate 
together until a balance is obtained. With regard to this 

* In what precedes, the planes of the coils have been always supposed 
to be parallel to each other : but it eyidently follows from the rea.soning 
here indicated that, if any set of paiallel tangents be di-awn to the lines of 
force and a curce be traced through the points of contact, an infinitely 
small coil would experience no inductive effect if it were placed with its 
centre anywhere in this curve, and with its plane parallel to the given set 
of tangents. 

41(j On the Conjugate Positions of two Circular Coils of Wire, 

combination, it may be observed that the greatest inductive 
effect occurs when the planes of the coils arc at the greatest 
distance from one another — and that as the planes approach, 
this eft'ect gradually diminishes, until, when they still are at 
some distance, it becomes nothing. 

Another, and perhaps more convenient, way of combining 
them is to place them, as in the last case, with their planes 
parallel and their axes coincident, the distance between them 
being equal to, or a little greater than, the radius of either coil : 
then, if their j)lanes are vertical, we may fix one of them in that 
position ; and if the other is capable of rotating round its ver- 
tical diameter, it will be found that when it has rotated through 
90° (that is, when the planes of the coils are at right angles) the 
inductive effects in the secondary circuit have ceased. If the 
coil is made to rotate through a few degrees to one side of this 
position, the currents induced in it will be in a certain direc- 
tion ; and if it is rotated to the other side, their direction will 
be found to be reversed. 

As with either of these combinations we could pass from 
sound to silence, some experiments were made in order to com- 
pare the rate of diminution of the induced currents with the 
movements of the coils in passing from a maximum to a mini- 
mum of inductive effects. 

For this purpose the coils were placed with their faces in con- 
tact and their axes coincident, the secondary one being joined 
in circuit with a reflecting galvanometer. In this position 
five observations were taken and the mean recorded. They 
were now separated until their planes were an inch iipart, a